Determine the inverse function of f ○ g(x). f (x) = 2 x + 9 and g (x) = −9 x + 8

Question

The inverse in this question is a function of y. What would "(f ○ g)−1(y) =" equal. I got the answer (-x+25)/18 (or 25/18-x/18). However, this answer is wrong. Should I just sub out the x to a y so that the answer is (f ○ g)−1(y) = (-y+25)/18, or am I just going about the whole question wrong?

Answer 1

Let's start from the beginning:

You need to find f O g(x), which can be found with this method:

f O g(x)= 2(-9x) + 9

=-18x + 9

 

Then, find the inverse by switching x and y

x= -18y + 9

x-9 = -18y

(x-9)/(-18)= y = f(g(x))^-1

 

Message me if you have further questions.