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

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

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Answer 1 · 2015-10-17T17:01:31

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

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

Explanation:

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

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

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

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

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

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

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

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