Confirm that f and g are inverses by showing that f (g (x)) = x and g (f (x)) = x. f (x) = quantity x minus seven divided by quantity x plus two. and g (x) = quantity negative two x minus seven divided by quantity x minus one.

You need to take the whole function of g (x) and plug it into every single x within f (x). Bit tricky, so it just means we need to be careful. Alright, so this is the first set-up - 2x-7 x-1 - 7 - 2x-7 x-1 + 2 So what You should do is make the top portion and the bottom portion all into one fraction. This means I need a common denominator. So to do this, I'll take x-1 as a common denominator and multiply it up into the numerator and the imaginary 1 denominator of - 7 and 2. Doing this I have: - 2x-7-7 (x-1) x-1 - 2x-7+2 (x-1) x-1 From here if I divide the top fraction and the bottom fraction, (x-1) will cancel out dueto me flipping the bottom fraction and multiplying. So that leaves me with: - 2x-7-7 (x-1) - 2x-7+2 (x-1) Now if I multiply everything out and combine like terms I will have: - 2x-7-7x+7 - 2x-7+2x-2 = - 9x - 9 = x So that is the first part. We have to check both ways to confirm they are actually inverses of each other, though. Take a look at this part and see if you can make sense of what I did.