Question

If g (x)=4x+7 and h (x)=x-6, find g (h(x))

Answer 1

Answer:

$g(h(x))=4x-17$.

Step-by-step explanation:

This is a problem of combination of functions. Let's find the combination of f(x) and g(x).

1. Write the full argument of g(x).

$g(x)=4x+7$

2. Insert the argument of h(x) as if it was an x value on g(x).

Argument of h(x): $x-6$.

$g(h(x))=4(x-6)+7$

3. Apply the associative property of multiplication to solve the parenthesis.

$g(h(x))=[(4)(x)+(4)(-6)]+7\\ \\g(h(x))=[4x+(-24)+7\\ \\g(h(x))=4x-24+7$

4. Simplify by adding.

$g(h(x))=4x-17$.

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