How to isolate for x in f(x)=x^2 + tan(pi*x/2) +5?

Question

How do you isolate for x? Everything I have tried results in one of the x variables being part of a trig function. (I am trying to find the inverse of this function, so if it is not possible to isolate for x, how do you find the inverse?

Answer 1

isolating for x or finding the inverse of the function in terms of f is very complicated. you were probably asked to find the derivative of the inverse; use chain rule:
f'(x)=2x+pi/2*sec^2(pi*x/2)
x'(f)=1/f'(x)
=1/(2x+pi/2*sec^2(pi*x/2))

Answer 2

First off, |x| <>1, else tan(pi*x/2) becomes undefined.
-pi/2 The curve does not pass the horizontal line test and thus the inverse is not a function.
x = 0.59816 [using my calculator]