Addition, Subtraction, Multiplication, Division of Functions
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Friends iss article mein aaj hum seekhenge do(two) functions ko kaise add karte hain, do(two) functions ko kaise subtract karte hain, do(two) functions ko kaise multiply karte hain, kisi scalar (ek real number) ki multiply kisi function se kaise karte hain, do(two) functions ko kaise divide karte hain etc.
Friends main aapko recommend karoonga ki pehle aap function se related mere previous articles ko padhiye kyuki ye waala article aapko tab hi sahi se samajh mein aayega jab aap fuctions se achchhi tarah se waakif (वाकिफ़) ho. Unn articles ko padhne ke liye inn blue links par click kijiye >>>
Chaliye ab point par aate hain.
Let's Begin...
Maan lijiye f : X → R, f(x) aur g : X → R, g(x) do(two) real functions hain aur X ⊂ R. Tab
(f + g) : X → R ko hum define karte hain (f + g)(x) = f(x) + g(x), for all x ∈ X.
Matlab, do(two) functions ka addition bhi ek function hota hai. Chaliye main isko detail mein batata hoon. Maan lijiye do(two) function f : X → R, f(x) aur g : X → R, g(x) hain jinke domain same hain aur domain ⊂ R. Maan lijiye ki function f : X → R ka rule f(x) hai aur function g : X → R ka rule g(x) hai. Ab inn dono functions ko agar add kiya jaaye to inke addition ko (f + g) : X → R se show karte hain aur iska rule dono functions, f : X → R aur g : X → R ke rules ko add karke aata hai matlab (f + g)(x) = f(x) + g(x).
Example ke liye aan lijiye f : N → R, f(x) = x2 aur g : N → R, g(x) = 2x + 1 tab (f + g) : N → R aur (f + g)(x) = f(x) + g(x)
= (x2) + (2x +1)
= x2 + 2x + 1
Maan lijiye f : X → R, f(x) aur g : X → R, g(x) do(two) real functions hain aur X ⊂ R. Tab
(f - g) : X → R ko hum define karte hain (f - g)(x) = f(x) - g(x), for all x ∈ X.
Matlab, do(two) functions ka subtraction bhi ek function hota hai. Chaliye main isko detail mein batata hoon. Maan lijiye do(two) function f : X → R, f(x) aur g : X → R, g(x) hain jinke domain same hain aur domain ⊂ R. Maan lijiye ki function f : X → R ka rule f(x) hai aur function
g : X → R ka rule g(x) hai. Ab inn dono functions ko agar add kiya jaaye to inke subtraction ko
(f + g) : X → R se show karte hain aur iska rule dono functions, f : X → R aur g : X → R ke rules ko subtract karke aata hai matlab (f - g)(x) = f(x) - g(x).
Example ke liye aan lijiye f : N → R, f(x) = x2 aur g : N → R, g(x) = 2x + 1 tab
(f - g) : N → R aur
(f - g)(x) = f(x) - g(x)
= (x2) - (2x +1)
= x2 - 2x - 1
Maan lijiye f : X → R, f(x) ek real function hai aur X ⊂ R and maan lijiye ki α ek scalar (matlab koi real number) hai . Tab αf : X → R ko hum define karte hain (αf)(x) = αf(x) , for all x ∈ X.
Matlab, ek functions ka kisi scalar se product (scalar product) bhi ek function hota hai. Chaliye main isko detail mein batata hoon. Maan lijiye ek function f : X → R, f(x) aur ek scalar α hai. Maan lijiye ki function f : X → R ka rule f(x) hai. Ab iss function ko aur scalar ko agar multiply kiya jaaye to inke multiplication (ya product) ko αf : X → R se show karte hain aur iska rule function,
f : X → R ke rule ko uss scalar se multiply karke aata hai matlab (αf)(x) = αf(x).
Example ke liye aan lijiye f : N → R, f(x) = x2 aur α = 4 tab αf : N → R aur
(αf)(x) = αf(x)
= 4(x2)
= 4x2
Maan lijiye f : X → R, f(x) aur g : X → R, g(x) do(two) real functions hain aur X ⊂ R. Tab
fg : X → R ko hum define karte hain (fg)(x) = f(x) . g(x), for all x ∈ X.
Matlab, do(two) functions ka multiplication bhi ek function hota hai. Chaliye main isko detail mein batata hoon. Maan lijiye do(two) function f : X → R, f(x) aur g : X → R, g(x) hain jinke domain same hain aur domain ⊂ R. Maan lijiye ki function f : X → R ka rule f(x) hai aur function
g : X → R ka rule g(x) hai. Ab inn dono functions ko agar multiply kiya jaaye to inke multiplication ko fg : X → R se show karte hain aur iska rule dono functions, f : X → R aur g : X → R ke rules ko multiply karke aata hai matlab (fg)(x) = f(x) . g(x).
Example ke liye aan lijiye f : N → R, f(x) = x2 aur g : N → R, g(x) = 2x + 1 tab fg : N → R aur
(fg)(x) = f(x) . g(x)
= (x2) . (2x +1)
= 2x3 + x2
Maan lijiye f : X → R, f(x) aur g : X → R, g(x) do(two) real functions hain aur X ⊂ R. Tab
(f/g) : X → R ko hum define karte hain (f/g)(x) = f(x) / g(x), for all x ∈ X and g(x) ≠ 0.
Matlab, do(two) functions ka division bhi ek function hota hai. Chaliye main isko detail mein batata hoon. Maan lijiye do(two) function f : X → R, f(x) aur g : X → R, g(x) hain jinke domain same hain aur domain ⊂ R. Maan lijiye ki function f : X → R ka rule f(x) hai aur function
g : X → R ka rule g(x) hai. Ab inn dono functions ko agar divide kiya jaaye to inke division ko
(f/g) : X → R se show karte hain aur iska rule dono functions, f : X → R aur g : X → R ke rules ko divide karke aata hai matlab (f/g)(x) = f(x) / g(x) aur g(x), 0 nahi hona chahiye.
Example ke liye aan lijiye f : N → R, f(x) = x2 aur g : N → R, g(x) = 2x + 1 tab (f/g) : N → R aur
(f/g)(x) = f(x) / g(x)
= (x2) / (2x +1) , x ≠ -1/2
Read Also:
I hope ki mera ye article aap ko pasand aaya hoga. Agar aap ko mera ye article pasand aaya ho to comment karke hame bata sakte hain. Aapke dwaara kiye gaye comment se hame iss tarah ke post/article ko likne ke liye motivation milta hai.
THANKS FOR READING THIS BLOG.
Friends main aapko recommend karoonga ki pehle aap function se related mere previous articles ko padhiye kyuki ye waala article aapko tab hi sahi se samajh mein aayega jab aap fuctions se achchhi tarah se waakif (वाकिफ़) ho. Unn articles ko padhne ke liye inn blue links par click kijiye >>>
Chaliye ab point par aate hain.
Let's Begin...
Addition of Two Real Functions
Maan lijiye f : X → R, f(x) aur g : X → R, g(x) do(two) real functions hain aur X ⊂ R. Tab
(f + g) : X → R ko hum define karte hain (f + g)(x) = f(x) + g(x), for all x ∈ X.
Matlab, do(two) functions ka addition bhi ek function hota hai. Chaliye main isko detail mein batata hoon. Maan lijiye do(two) function f : X → R, f(x) aur g : X → R, g(x) hain jinke domain same hain aur domain ⊂ R. Maan lijiye ki function f : X → R ka rule f(x) hai aur function g : X → R ka rule g(x) hai. Ab inn dono functions ko agar add kiya jaaye to inke addition ko (f + g) : X → R se show karte hain aur iska rule dono functions, f : X → R aur g : X → R ke rules ko add karke aata hai matlab (f + g)(x) = f(x) + g(x).
Example ke liye aan lijiye f : N → R, f(x) = x2 aur g : N → R, g(x) = 2x + 1 tab (f + g) : N → R aur (f + g)(x) = f(x) + g(x)
= (x2) + (2x +1)
= x2 + 2x + 1
Subtraction of Two Real Functions
Maan lijiye f : X → R, f(x) aur g : X → R, g(x) do(two) real functions hain aur X ⊂ R. Tab
(f - g) : X → R ko hum define karte hain (f - g)(x) = f(x) - g(x), for all x ∈ X.
Matlab, do(two) functions ka subtraction bhi ek function hota hai. Chaliye main isko detail mein batata hoon. Maan lijiye do(two) function f : X → R, f(x) aur g : X → R, g(x) hain jinke domain same hain aur domain ⊂ R. Maan lijiye ki function f : X → R ka rule f(x) hai aur function
g : X → R ka rule g(x) hai. Ab inn dono functions ko agar add kiya jaaye to inke subtraction ko
(f + g) : X → R se show karte hain aur iska rule dono functions, f : X → R aur g : X → R ke rules ko subtract karke aata hai matlab (f - g)(x) = f(x) - g(x).
Example ke liye aan lijiye f : N → R, f(x) = x2 aur g : N → R, g(x) = 2x + 1 tab
(f - g) : N → R aur
(f - g)(x) = f(x) - g(x)
= (x2) - (2x +1)
= x2 - 2x - 1
Multiplication of a Real Functions by a Scalar
Maan lijiye f : X → R, f(x) ek real function hai aur X ⊂ R and maan lijiye ki α ek scalar (matlab koi real number) hai . Tab αf : X → R ko hum define karte hain (αf)(x) = αf(x) , for all x ∈ X.
Matlab, ek functions ka kisi scalar se product (scalar product) bhi ek function hota hai. Chaliye main isko detail mein batata hoon. Maan lijiye ek function f : X → R, f(x) aur ek scalar α hai. Maan lijiye ki function f : X → R ka rule f(x) hai. Ab iss function ko aur scalar ko agar multiply kiya jaaye to inke multiplication (ya product) ko αf : X → R se show karte hain aur iska rule function,
f : X → R ke rule ko uss scalar se multiply karke aata hai matlab (αf)(x) = αf(x).
Example ke liye aan lijiye f : N → R, f(x) = x2 aur α = 4 tab αf : N → R aur
(αf)(x) = αf(x)
= 4(x2)
= 4x2
Multiplication of Two Real Functions
Maan lijiye f : X → R, f(x) aur g : X → R, g(x) do(two) real functions hain aur X ⊂ R. Tab
fg : X → R ko hum define karte hain (fg)(x) = f(x) . g(x), for all x ∈ X.
Matlab, do(two) functions ka multiplication bhi ek function hota hai. Chaliye main isko detail mein batata hoon. Maan lijiye do(two) function f : X → R, f(x) aur g : X → R, g(x) hain jinke domain same hain aur domain ⊂ R. Maan lijiye ki function f : X → R ka rule f(x) hai aur function
g : X → R ka rule g(x) hai. Ab inn dono functions ko agar multiply kiya jaaye to inke multiplication ko fg : X → R se show karte hain aur iska rule dono functions, f : X → R aur g : X → R ke rules ko multiply karke aata hai matlab (fg)(x) = f(x) . g(x).
Example ke liye aan lijiye f : N → R, f(x) = x2 aur g : N → R, g(x) = 2x + 1 tab fg : N → R aur
(fg)(x) = f(x) . g(x)
= (x2) . (2x +1)
= 2x3 + x2
Division(Quotient) of Two Real Functions
Maan lijiye f : X → R, f(x) aur g : X → R, g(x) do(two) real functions hain aur X ⊂ R. Tab
(f/g) : X → R ko hum define karte hain (f/g)(x) = f(x) / g(x), for all x ∈ X and g(x) ≠ 0.
Matlab, do(two) functions ka division bhi ek function hota hai. Chaliye main isko detail mein batata hoon. Maan lijiye do(two) function f : X → R, f(x) aur g : X → R, g(x) hain jinke domain same hain aur domain ⊂ R. Maan lijiye ki function f : X → R ka rule f(x) hai aur function
g : X → R ka rule g(x) hai. Ab inn dono functions ko agar divide kiya jaaye to inke division ko
(f/g) : X → R se show karte hain aur iska rule dono functions, f : X → R aur g : X → R ke rules ko divide karke aata hai matlab (f/g)(x) = f(x) / g(x) aur g(x), 0 nahi hona chahiye.
Example ke liye aan lijiye f : N → R, f(x) = x2 aur g : N → R, g(x) = 2x + 1 tab (f/g) : N → R aur
(f/g)(x) = f(x) / g(x)
= (x2) / (2x +1) , x ≠ -1/2
Read Also:
- What is Set ?
- Types of Set
- Venn Diagrams
- Intersection of Sets
- Difference of Sets
- Symmetric Difference of Sets
- What are Intervals ?
- What is Cartesian Product ?
- What is a Function?
- Coordinate (Cartesian) System - Coordinate Geometry
- Arithmetic Progression (AP)
- How to Solve Quadratic Equation using Quadratic Formula ?
- What is polynomial and equation ?
- What is Euclid's Division Lemma (algorithm) ?
- What is complex number, real number, irrational number, rational number, integer, whole number, natural number and number line?
- What is odd number, even number, prime number, composite number, co-prime number, factor and multiple ?
I hope ki mera ye article aap ko pasand aaya hoga. Agar aap ko mera ye article pasand aaya ho to comment karke hame bata sakte hain. Aapke dwaara kiye gaye comment se hame iss tarah ke post/article ko likne ke liye motivation milta hai.
THANKS FOR READING THIS BLOG.
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