If #f(x)=x+3# how do you find the inverse?

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Answer 1 · 2016-11-25T18:59:37

Please see the explanation.

Given: Find the inverse of #f(x) = x + 3#

Substitute #f^-1(x)# for every x:

#f(f^-1(x)) = f^-1(x) + 3#

By definition, #f(f^-1(x)) = x#:

#x = f^-1(x) + 3#

Solve for #f^-1(x)#

#f^-1(x) = x - 3#

Check by verifying that f(f^-1(x)) = f^-1(f(x)) = x:

#f(f^-1(x)) = (x - 3) + 3 = x#

#f^-1(f(x)) = (x + 3) - 3 = x#

This checks.