Given the functions fx 7x 6 and a fogx b go0x c fofx d

Given the functions f{x) = 7x - 6 and = (a) {fog){x) = (b) (go/0(x) = (c) {fof)(x) = (d) (gog)(x) =

f(x) = 7x -6 , g(x) = -x²

a) (f o g)(x)

==> f(g(x))

==> f(-x²)

==> 7(-x²) -6

==> -7x² - 6

Hence (f o g)(x) = -7x² - 6

b) (g o f)(x)

==> g(f(x))

==> g(7x -6)

==> -(7x - 6)²

==> -(49x² -84x + 36)

==> -49x² + 84x - 36

Hence (g o f)(x) = -49x² + 84x - 36

c) (f o f)(x)

==> f(f(x))

==> f(7x -6)

==> 7(7x -6) -6

==> 49x - 42 -6

==> 49x - 48

Hence (f o f)(x) = 49x - 48

d) (g o g)(x)

==> g(g(x))

==> g(-x²)

==> - (-x²)²

==> -x⁴

Hence (g o g)(x) = -x⁴