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

Oct 17, 2015

In order to solve (g o f)(x) for $f \left(x\right) = 2 x - 5$ and $g \left(x\right) = {x}^{2} - 3$, the f(x) function must be substituted into the g(x) function.

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

#### Explanation:

In order to solve (g o f)(x) for $f \left(x\right) = 2 x - 5$ and $g \left(x\right) = {x}^{2} - 3$, the f(x) function must be substituted into the g(x) function.

(g o f)(x) = ${\left(2 x - 5\right)}^{2} - 3$

(g o f)(x) = $\left(2 x - 5\right) \left(2 x - 5\right) - 3$

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

(g o f)(x) = $4 {x}^{2} - 20 x + 25 - 3$

(g o f)(x) = $4 {x}^{2} - 20 x + 22$