let f (x)=4X-2 and g (X)=-2x^2+8 (a) find f^-1 (X) (b) find (f o g)(1)

let f (x)=4X-2 and g (X)=-2x^2+8

(a) find f^-1 (X)

(b) find (f o g)(1)

Answered Same DayDec 22, 2021

Answer To: let f (x)=4X-2 and g (X)=-2x^2+8 (a) find f^-1 (X) (b) find (f o g)(1)

David answered on Dec 22 2021

124 Votes

let f (X)= 4X-2 and g (X)= -2X^2+8
(a) find f^-1 (X)
Let,
f^-1(X)=Y
=> X = f(Y)
=> X = 4Y-2
=> Y = (X+2)/4
So,
f^-1(X)= Y = (X+2)/4.
(b) find (f o g)(1)
Note that,
(fog)(X) = f(g(X)) = f(-2X^2+8) = 4*(-2X^2+8)-2
= -8X^2 +30
So,
(f o g)(1) = -8 +30 = 22

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let f (x)=4X-2 and g (X)=-2x^2+8 (a) find f^-1 (X) (b) find (f o g)(1)

Answer To: let f (x)=4X-2 and g (X)=-2x^2+8 (a) find f^-1 (X) (b) find (f o g)(1)

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