Question

What is (f•g)(x)? F(x)= x^2-2x+3 G(x)=x^3-4

Answer 1

STEP - BY - STEP EXPLANATION

What to find?

(f•g)(x)

Given:

`\begin{gathered} f(x)=x^2-2x+3 \\ \\ g(x)=x^3-4 \end{gathered}`

Step 1

Define (f. g)(x)

`(f.g)(x)=f(x).g(x)`

Step 2

Substitute the functions into the above.

`(f.g)(x)=(x^2-2x+3)(x^3-4)`

Step 3

Open the parenthesis and simplify.

`(f.g)(x)=x^5-4x^2-2x^4+8x+3x^3-12`
`=x^5-2x^4+3x^3-4x^2+8x-12`

ANSWER

`(f.g)(x)=x^5-2x^4+3x^3-4x^2+8x-12`