Find the inverse of this equation....?

Question

Let f(x) = 6 + x^2 + tan(πx/2), where -1 < x < 1

A.) Find f ^ -1 (6)

B.) Find f(f ^ -1(8))

Answer 1

checking the graph .. . . this function is one-to-one on the provided interval

thus an inverse exist.

f^(-1)(6) = w

means

f(w) = 6

6 = 6 + w^2 + tan(πw/2)

0 = w^2 + tan(πw/2)

by inspection .. . .. .

w = 0

b. f(f^(-1)(8)) = 8

by property of inverses