Eliza Berry

2023-03-03

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

Kiara Rollins

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) = ${\left(2x-5\right)}^{2}-3$
(g o f)(x) = $\left(2x-5\right)\left(2x-5\right)-3$
by FOIL (First Outer Inner Last)
$\left(2x-5\right)\left(2x-5\right)=\left(2x\right)\left(2x\right)-10x-10x+25$
$4{x}^{2}-20x+25$
(g o f)(x) = $4{x}^{2}-20x+25-3$
(g o f)(x) = $4{x}^{2}-20x+22$

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