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of Two functions are said to be inverses each other if fig) I=(9) f(x) where I is the identity function, ie I(x) = x V x ie (fog)(x) = I & (gof)(x) = I x Now, (fog)(x) = f(g(x)) = f(x+3) = 2 (21³)-3 = x+3-3 = x ⇒ fog(x) = I(x) \x Also, (gof)(x) = g(f(x)) =9 (2x-3) 2x-3+3 2 gof (x) = (x) Fx ⇒ 1&9 are inverses of each other. 2x 2 = = x

of Two functions are said to be inverses each other if fig) I=(9) f(x) where I is the identity function, ie I(x) = x V x ie (fog)(x) = I & (gof)(x) = I x Now, (fog)(x) = f(g(x)) = f(x+3) = 2 (21³)-3 = x+3-3 = x ⇒ fog(x) = I(x) \x Also, (gof)(x) = g(f(x)) =9 (2x-3) 2x-3+3 2 gof (x) = (x) Fx ⇒ 1&9 are inverses of each other. 2x 2 = = x

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Two functions are said to be inverses. each other if of f(9) I=(9) f(x) where I is the identity function. ie. I(x) = xxx ie (fog)(x) = I & (gof)(x) = I x Now, (fog)(x) = f(g(x)) = f (x+³) = 2(x+³) - 3 = x+3-3 =x ⇒ fog(x)= I(x)\x Also, (gof)(x) = g(f(x)) =9 (2x-3) = 2x-3+3 = 22 gof (x)= I(x) √x ⇒ f &9 are inverses of each other. of Two functions are said to be inverses each other if = x f(g)= I=(9) f(x) where I is the identity function, ie I(x) = x V x ie (fog)(x) = I & (gof)(x) = I x x Now, (fog)(x) = f(g(x)) = f (x+3) = 2 (2+5)-3 = x+3-3 =x ⇒ fog(x) = I(x)\x
Transcribed Image Text:Two functions are said to be inverses. each other if of f(9) I=(9) f(x) where I is the identity function. ie. I(x) = xxx ie (fog)(x) = I & (gof)(x) = I x Now, (fog)(x) = f(g(x)) = f (x+³) = 2(x+³) - 3 = x+3-3 =x ⇒ fog(x)= I(x)\x Also, (gof)(x) = g(f(x)) =9 (2x-3) = 2x-3+3 = 22 gof (x)= I(x) √x ⇒ f &9 are inverses of each other. of Two functions are said to be inverses each other if = x f(g)= I=(9) f(x) where I is the identity function, ie I(x) = x V x ie (fog)(x) = I & (gof)(x) = I x x Now, (fog)(x) = f(g(x)) = f (x+3) = 2 (2+5)-3 = x+3-3 =x ⇒ fog(x) = I(x)\x
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