For the given functions fand g find each of the following co

For the given functions fand g, find each of the following composite functions. f(x) = 4x + 3 g{x) = 2x2-1

Solution

f(x) = 4x + 3

g(x) = 2x² - 1

a) (f o g)(4)

==> f(g(4))

==> f(2(4)² - 1)

==> f(31)

==> 4(31) + 3

==> 127

Hence (f o g)(4) = 127

b) (g o f)(2)

==> g(f(2))

==> g(4(2) + 3)

==> g(11)

==> 2(11)² - 1

==> 241

Hence (g o f)(2) = 241

c) (f o f)(1)

==> f(f(1))

==> f(4(1) + 3)

==> f(7)

==> 4(7) + 3

==> 31

Hence (f o f)(1) = 31

d) (g o g)(0) = g(g(0))

==> g(2(0)² - 1)

==> g(-1)

==> 2(-1)² - 1

==> 1

Hence (g o g)(0) = 1