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. 

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
$f(x)=x^{2} -4x-3$
$g(x)=\frac{x+3}{4}$

So we find
$f(g(x))=f(g(9))=(\frac{9+3}{4})^2 - 4(\frac{9+3}{4})-3$
$=3^2 - 4(3)-3$
$= 9-12-3=-6$
Now we want to find the solution when x is 9 so we plug in a 9 whenever we see an x