How do you determine whether the function #q(x)=(x-5)^2# has an inverse and if it does, how do you find the inverse function?

1 Answer
Mar 29, 2017

No inverse function

Explanation:

The function can be rewritten as an equation: #y=(x-5)^2#. To find the inverse function, we solve for #x# in terms of #y#.

#y=(x-5)^2#
#+-sqrt(y)=x-5#
#x=+-sqrt(y)+5#

The inverse function of #q(x)# then should be #q^-1(x)=+-sqrt(x)+5# (we replaced the #y# in the equation for #x#). However, remember that, for functions, for any value #x#, there is only one value #y# for that #x#. This is clearly not the case here, since, for most values of #x# (except #x=0#), there are two possible #y# values because of the #+-# sign.

Therefore, there are no inverse functions for #q(x)#.