Find the inverse function of f, and state the domain and range of f and f-1.

Question

(a) Find the inverse function of f, (b) graph f and f^-1 on the same set of coordinate axes, (c) describe the relationship between the graphs, and (d) state the domain and range of f and f^-1.

f (x) = √x

Answer 1

Step 1:

a)

The function is

Consider

Find the inverse function.

Interchange the variables and .

Squaring on each side.

The inverse function is .

Step 2:

b)

The graph of the functions are and .

Step 3:

The function is .

The inverse function is .

Observe the graph, the relationship between functions and are symmetric about .