Given fx 3x2 2 and gx 7 12x2 find the following expressio

Given f(x) = 3x^2 - 2 and g(x) = 7 -1/2x^2, find the following expressions. (f composite g)(4) (g composite f)(2) (f composite f)(1) (g composite g)(0) (f composite g)(4) = (Simplify your answer.)

Solution

f(x) = 3x^2 -2 and g(x) = 7 -1/2x^2

a).

(f o g)(4) = f(g(4))

= f (7 -1/2(4)^2)

=f(7 -16/2)

=f(7 -8)

=f(-1)

= 3(-1)^2 -2

=1

so (f o g)(4) = 1

b).

(gof)(2) = g(f(2))

= g(3(2)^2 -2)

=g(3.4 -2)

= g(12-2)

=g(10)

= 7 - (10)^2/2

= 7 -100/2

=7-50

=-43