Question

Can anyone tell me how to do this? Step by step

Answer 1

9x^2 + 42x + 16

Explanation:

f(g(x))

Plug in the expression for g(x)

f(g(x)) = f(-3x - 5)

f(x) = x^2 - 4x - 9

For every x in f(x) replace it with -3x - 5

f(-3x - 5) = (-3x - 5)^2 - 4(-3x -5) -9

Expand

f(-3x - 5) = (9x^2 + 30x + 25) + (12x + 20) - 9

Combine like terms

f(-3x - 5) = 9x^2 + 42x + 16

f(g(x)) = 9x^2 + 42x + 16

Answer 2

Explanation:

f(x)=x^2-4x-9

g(x)=-3x-5

so when f(g(x)) that x is a number

-3x-5 equals the number in f(x) so that x is -3x-5

f(-3x-5) and if f(x)=x^2-4x-9

then inserting in -3x-5 for x in f(x) and distrubute

(-3x-5)^2-4(-3x-5)-9

9x^2+42x+36

I hope that helps :)