Question

f(x)=1/(x+2)
f^-1(x)= (1/x)-2
Find (f^-1of)(x)

Answer 1

Note that \((f^{-1}\circ f)(x) = f^{-1}(f(x))\). Since \( f^{-1}(x) = \dfrac{1}{x}-2 \), we see that \(f^{-1}(f(x)) = \dfrac{1}{f(x)}-2\). Now substitute \(f(x)=\dfrac{1}{x+2}\) into this and simplify. What do you get when you do this? :-)

Answer 2

f−1(f(x)) = 1/(1/(x+2))−2. I am not too sure how to simplify this further

Answer 3

Hint: 1/(1/(x+2)) = x+2. So what do you get now?

Answer 4

oh, x+2-2=x
so the 1's just cancel each other out?

Answer 5

POP, POP!

Answer 6

@Dylan548 Yup, that's correct. Does that make sense?

Answer 7

Yes it does, I very much appreciate your help!!