Question

If f(x) = 2x - 5 and g(x) = x^2 - 3, what is (g o f)(x)?

Answer 1

In order to solve (g o f)(x) for `f(x) = 2x - 5` and `g(x) = x^2 - 3`, the f(x) function must be substituted into the g(x) function.

The simplification of the function is
(g o f)(x) = `4x^2 -20x + 22`

Explanation:

In order to solve (g o f)(x) for `f(x) = 2x - 5` and `g(x) = x^2 - 3`, the f(x) function must be substituted into the g(x) function.

(g o f)(x) = `(2x - 5)^2 - 3`

(g o f)(x) = `(2x - 5)(2x - 5) - 3`

by FOIL (First Outer Inner Last)
(2x - 5)(2x - 5) = (2x)(2x) - 10x - 10x + 25
`4x^2 -20x + 25`

(g o f)(x) = `4x^2 -20x + 25 - 3`

(g o f)(x) = `4x^2 -20x + 22`