"How to find (gof)(x) given f(x)=x−1 and g(x)=x2+2x−8?" was answered by our experts

Brisa Lyons

Answered question

2023-01-17

How to find

(g o f) (x)

given

f (x) = x - 1

and

g (x) = x^{2} + 2 x - 8

eyrurin3wj

Beginner2023-01-18Added 10 answers

The following equation provides another notation:

(g o f) (x) = g (f (x))

We substitute

g (x) = x^{2} + 2 x - 8

on the right side but we write

(f (x))

everywhere that there is an x:

(g o f) (x) = {(f (x))}^{2} + 2 (f (x)) - 8

Substitute

x - 1

for

f (x)

(g o f) (x) = {(x - 1)}^{2} + 2 (x - 1) - 8

Expand the square:

(g o f) (x) = x^{2} - 2 x + 1 + 2 (x - 1) - 8

Use the distributive property:

(g o f) (x) = x^{2} - 2 x + 1 + 2 x - 2 - 8

Combine like terms:

(g o f) (x) = x^{2} - 9 \leftarrow

answer

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