determine an equation f^-1
f(x)=1/(x+1)
I know that I need to switch x and y values. i am just not sure on how to solve for x

Question

determine an equation f^-1
f(x)=1/(x+1)
I know that I need to switch x and y values. i am just not sure on how to solve for x

campbell_st · Answer

ok... frist thing you need to know is that  x cannot be negative 1

so write your equation as 

$$x = \frac{1}{y + 1}$$

now make y the subject.

anonymous · Answer

I dont want to divide y out though, right?

campbell_st · Answer

ok... simple step mutliply both sides by (y + 1)

campbell_st · Answer

what do you get

anonymous · Answer

then i would divide by x then subtract 1 from both sides right?

anonymous · Answer

(1/x)-1 is what i got

campbell_st · Answer

thats correct so you inverse is
$$f^{-1}(x) = \frac{1}{x} - 1$$

the restriction in the inverse is that y cannot equal - 1

anonymous · Answer

awesome! I am really bad at this solving for y part of these problems
Thanks for the help!

campbell_st · Answer

glad to help