How do you find the inverse of #f(x)=3x-5# and is it a function?

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Answer 1 · 2018-03-10T20:28:44

#f^-1(x) = (5+x)/3#

The inverse of a function #f(x)# is another function, #f^-1(x)#, which reverses #f(x)#. (So yes it is a function)

We can find it by first writing out the equation #x=f(y)#

#x=3y-5#

#f(y)# is just the expression #f(x)# but with #y's# instead of #x's#

Rearrange to make #y# the subject (isolate #y# to be on its own)

In this case, add #5# to both sides and divide both sides by #3#

#y=(5+x)/3#

Finally, replace #y# with #f^-1(x)#

#f^-1(x) = (5+x)/3#