Question

Find the inverse function f^-1 of the function f. What is the domain of f^-1? What is its range?

f(x) = 5 tan (10x-2)

Answer 1

switch variables and solve for y:
x = 5tan(10y-2)
x/5 = tan(10y-2)
10y-2 = arctan(x/5)
y = (arctan(x/5)+2)/10

In order for tan(z) to have an inverse, -π/2 < z < π/2
So, we need to restrict f(x) so its domain is
-π/2 < 10x-2 < π/2
2-π/2 < 10x < 2+π/2
(2-π/2)/10 < x < (2+π/2)/10

Now you can see what the domain and range of the f^-1 are.