What is the inverse of #h(x) = 5x + 2#?

2 Answers
Jul 30, 2016

#y = 1/5x - 2/5#

Explanation:

We have

#y = 5x+2#

When we invert a function what we are doing is reflecting it across the line #y=x# so what we do is swap the x and y in the function:

#x = 5y + 2#

#implies y = 1/5x - 2/5#

Jul 30, 2016

The inverse of a function #h(x)# is a function #f# such that the composition #h(f)=identity# or, in other words, such that #h(f(x))=x#

Explanation:

Given this definition, we apply #h# in the point #f(x)#; so #h(f(x))=5f(x)+2#. But this must be #h(f(x))=5f(x)+2=x# and hence #5(f(x))=x-2#, and then #f(x)=(x-2)/5=1/5x-2/5#