What is the inverse function of #f(x)=x+1# and how do you find #f^-1(2)#?

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Answer 1 · 2016-01-14T00:21:28

#f^(-1)(x) = x-1#

#f^(-1)(2) = 1#

#f^(-1)(x)# is a function such that #f(f^(-1))(x) = f^(-1)(f(x)) = x#

Then, if #y = f^(-1)(x)# we can apply #f(x)# to both sides to get

#f(y) = f(f^(-1)(x)) = x#

In the given function, this translates to

#y + 1 = x#

Then, as #y = f^(-1)(x)#, we can simply solve for #y# and substitute.

#y = x-1#

#=> f^(-1)(x) = x-1#

And so #f^(-1)(2) = 2-1 = 1#