Given fx 9x 7 and gx 3 squareroot x find the following ex

Given f(x) = 9/x + 7 and g(x) = 3 squareroot x, find the following expressions. (f compositefunction g)(4) (g compositefunction f)(2) (f compositefunction f)(1) (g composite function g)(0) (f compositefunction g)(4) = (Type an exact answer, using radicals as needed. Simplify your answer.) (g composite function f)(2) = (Type an exact answer, using radicals as needed. Simplify your answer.) (f compositefunciton f)(1) = (Type an exact answer, using radicals as needed. Simplify your answer.) (g compositefunction g) (0) = (Type an exact answer, using radicals as needed. Simplify your answer.)

Solution

f(x) = 9/(x +7) ; g(x) = (x)^1/3

(f o g)(x) = 9/( x^1/3 +7)

(g o f)(x) = (9/x+7)^1/3

(f o f)(x) = 9/( 9/(x+7) +7) = 9(x+7)/(9 +7x +49) = (9x + 63)/( 7x + 58)

( g o g)(x) = ((x)^1/3)^1/3

a) (f o g)(4) = 9/( 4^1/3 +7)

b) ( g of)(2) = (9/2+7)^1/3 = 1

c) ( f o f)(1) = (9*1 + 63)/( 7*1 + 58) = 72/65

d) (g o g)(0) = ((0)^1/3)^1/3 = 0