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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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