Let F(x)=2x+4 and G(x)=4x^2 +4x

Question

After simplifying

(F o G) (x)=

When I did it on my paper I plugged in the 4x^2+4x in as F(4x^2+4x) and then fully plugged it in with it looking like 2(4x^2+4x)+4 and when I was multiplying I got 8x^2+8x+4 but I think I might be wrong and do not know where I went wrong if I got my work wrong on paper.

Answer 1

Your answer of 8x^2+8x+4 is correct. You could potentially simplify further by removing a greatest common factor of 4 to get 4(2x^2+2x+1)

If you are ever in doubt, you can always plug in a sample x value (such as x=0) into the original problem and your answer. If those numbers are equal, you have the correct equation. Sometimes, you are also able to factor out the squared function similar to when you solve a quadratic function, but this equation does not work for that.