Math Questions and Answers

Start Your Free Trial

How do you find the inverse in f^-1(x) notation for f(x) = 3 radical x+3? I understand how to find the inverse of a function for most problems, but this one I just can't figure out. And for the 3 radical x+3, I don't know whether it's said 3 radical x+3 or 3 square root of x+3 so sorry for that if it's confusing.  Thanks

Expert Answers info

Eric Bizzell eNotes educator | Certified Educator

briefcaseTeacher (K-12)

calendarEducator since 2011

write3,158 answers

starTop subjects are Math, Science, and Business

Find the inverse of `f(x)=3sqrt(x+3)` :

The typical way to find the inverse is to exchange x and y and solve for y:





But there is a problem. The original function had a domain restriction; `x>=-3` . We must take this into account. The range of the original function was `y>=0` so the domain of the inverse is `x>=0` .

If `f(x)=3sqrt(x+3)` then the inverse `f^(-1)(x)=1/9x^2-3,x>=0`

The graph of the function (green) and the inverse (red):

Note that as expected the graphs are reflections across the line y=x.

check Approved by eNotes Editorial