Question

Let f(x) = -3x² - 1 and g(x) = -5x. Find f(g(x)).

-15x²-1
0-75x²-1
15x²+5
15x² + 5x

Answer 1

`\huge{ \boxed{f(g(x)) = - 75 {x}^(2) - 1}}`

Explanation:

To find f(g(x)), substitute g(x) into f(x). That is for every x found in f(x), replace it by g(x) and solve.

`f(x) = - 3 {x}^(2) - 1 \\ g(x) = - 5x`

`f(g(x) )= - 3 ({ - 5x})^(2) - 1 \\ = - 3(25 {x}^(2) ) -1 \\ = - 75 {x}^(2) - 1 \: \: \: \: \: \:`

We have the final answer as

`\bold{f(g(x)) = - 75 {x}^(2) - 1}`