SOLUTION: In reference to Inverse Functions: How do you determine when to use the "short cut" method when trying to find the inverse of a function? For example, f(x) y = (x3+8)/3 so, we cu

Question 15349: In reference to Inverse Functions: How do you determine when to use the "short cut" method when trying to find the inverse of a function? For example, f(x) y = (x3+8)/3 so, we cubed it, added 8, and then divided by 3. If you undo it in reverse order (multiply 3, minus 8, cube root) it becomes the inverse. Why won't this work on all the problems? Thank you in advance!
Found 2 solutions by khwang, rapaljer:
Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
You are right for the inverse of
f(x)= y =
to get
y =

But use ^ for exponent and parentehsis for grouping terms next time.
If the original function is constructed by elementary invertible
function (such as addition, multiplication,...) , we only need to
apply reverse process step by step to get the inverse function.

Since y=f(x)= .. then
= ..
(if each is invertible.]
By for some functions such as y = x/(x^2+1) (or the functions containing
some transcendental functions as trig or log )
is not so easy to get 1st inverse. I suggest that you try.

Anyway, you have got good idea and good luck!!!
Kenny

Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
I'll just BET that this question was raised by one of MY own students, with reference to #17 on page 329 of my College Algebra: One Step at a Time!!! Am I right??? Congratulations on a GREAT question, and thanks to Kenny for a great answer. "Invertible" steps! That's what you call it.

R^2 at Seminole Community College
Sanford, Florida
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