Question

Given that f(x) = x2 − 4x − 3 and g(x) = the quantity of x plus three, over four, solve for f(g(x)) when x = 9. 

−6

3

6

9

Answer 1

Hello! To find the composition of functions we want to take all the x values in f(x) and replace them with g(x). Then to solve for a specific value, we plug in that value for x. Let's look at the steps below

`f(x)=x^(2) -4x-3`

`g(x)=(x+3)/(4)`

So we find

`f(g(x))=f(g(9))=((9+3)/(4))^2 - 4((9+3)/(4))-3`

`=3^2 - 4(3)-3`

`= 9-12-3=-6`
Now we want to find the solution when x is 9 so we plug in a 9 whenever we see an x