Question

F(x)=2x+1 and g(x)=x^2-7, find (f g) (x)

Answer 1

(f-g)(x) = - x² + 2x + 8

Explanation:

f(x) = 2x+1

g(x) = x² - 7

To find (f-g)(x) subtract g(x) from f(x)

That's

(f-g)(x) = 2x + 1 - ( x² - 7)

Remove the bracket

We have

(f-g)(x) = 2x + 1 - x² + 7

Simplify

We have the final answer as

(f-g)(x) = - x² + 2x + 8

Answer 2

The answer is (f o g)(x) = 2x^2 - 13

In order to find a composite function, you take the first letter (in this case f) and use that equation. You then remove the variable and put in the second letter (g).

f(x) = 2x + 1 ----> Remove variable.

f(x) = 2( ) + 1 ----> Insert g(x)

(f o g)(x) = 2(x^2 - 7) + 1 ----> Distribute

(f o g)(x) = 2x^2 - 14 + 1 ----> Simplify

(f o g)(x) = 2x^2 - 13