Eliza Berry

2023-03-03

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

Kiara Rollins

Beginner2023-03-04Added 6 answers

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

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

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

by FOIL (First Outer Inner Last)

$(2x-5)(2x-5)=(2x)(2x)-10x-10x+25$

$4{x}^{2}-20x+25$

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

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

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

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

by FOIL (First Outer Inner Last)

$(2x-5)(2x-5)=(2x)(2x)-10x-10x+25$

$4{x}^{2}-20x+25$

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

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