given fx2x21 and gx712x2 find fg4 Given fx 2x2 1 and gx 7

Given f(x) = 2x^2 - 1 and g(x) = 7 - 1/2x^2, find the following expressions. (a) (f o g)(4) (b) (g o f)(2) (c) (f o f)(1) (d) (g o g)(0) (a) (f o g) (4) =

Solution

Dear Student Thank you for using Chegg f(x) = 2x^2 - 1 g(x) = 7 - (1/2)x^2 a) fog(x) = 2 {7 - (1/2)x^2}^2 - 1 fog(4) = 2{7 - (1/2)(4)^2}^2 - 1   = 1 b) gof(x) = 7 - (1/2)(2x^2 -1)^2 gof(2) = 7 - (1/2)(2*2^2 -1)^2 = -17.5 c) fof(x) = 2(2x^2-1)^2 -1 fof(1) = 2*(2*1^2 - 1)^2 - 1 = 1 d) gog(x) = 7-(1/2)(7-(1/2)x^2) gog(0) = 7-(1/2)(7-(1/2)(0)^2)^2 = -17.5