How do i find (fog)(x) = 0

Question

How do i find (fog)(x) = 0 given that f(x) = 2x^2 - 18 and g(x) = x + 2. I came up with the solution of square root of five. But apperently this answer is incorrect.

Answer 1

Oliver, here’s how to do it.

first write f(x)

f(x) = 2x^2 - 18

now substitute g(x) for x

f(g(x)) = 2g(x)² - 18

now substitute the formula for g(x)

f(x+2) = 2(x+2)²-18

I’m sure an Algebra 2 student knows how to evaluate and solve, but I’ll give a hint for the ones who are reading ahead.

Multiply it out

f(x+2) = 2(x²+4x+4)-18

= 2x²+ 8x + 8 - 18

= x²+4x-5

We want that set to zero.

0 = x²+4x-5

Now solve that for x

If you have any questions, please ask.