Question

Consider the function. f(x) = x^2 − 1, x ≥ 1

(a) Find the inverse function of f.

f ^−1(x) =

(b) Graph f and f ^−1 on the same set of coordinate axes.

(c) Describe the relationship between the graphs. The graphs of f and f^−1 are reflections of each other across the line ____answer here___________.

(d) State the domain and range of f and f^−1. (Enter your answers using interval notation.)

Domain of f

Range of f

Domain of f ^−1

Range of f ^−1

Answer 1

(a)

we are given

we can set f(x)=y

now, we can switch x and y

we can solve for y

so, we get

.............Answer

(b)

Graph:

(c)

Since, f and f^-1 are inverse of each other

so, both graphs are reflected about y=x line

Across y=x line

(d)

Domain:

It is all possible values of x for which any function is defined

Range:

It is all possible values of y for which any function is defined

Domain:

It is all possible values of x for which any function is defined

Range:

It is all possible values of y for which any function is defined