I do not understand how to solve this type of equation

Question

f(x)=x^2+1,g(x)=x-6. Find (f0g)(3) and (g0f)(-2)

Answer 1

Firstly, we find the interior functions then plug them into the outer one. Terms that A physicist trying to explain math :-) Bear with me Jonelle.

(fog)(3) == First find g(3), then put this as an input to f(x)

Let's do it...

g(3) = 3-6 = -3

Then, feed -3 into f(x), f(-3) = (-3)² + 1 = 10

So, fog(3) = 10

What about the other?

Same thing...

We have got to find f(-2) first.

f(-2) = (-2)² + 1 = 5, feed this into 'g'

g(5) = 5-6 = -1

So (g0f)(-2) = -1