How to find domain and range of the inverse of a relation

Practice Questions

SAT Math › How to find domain and range of the inverse of a relation

Questions

10

1

What is the range of the function y = _x_2 + 2?

2

What is the smallest value that belongs to the range of the function $f(x)=2|4-x|-2$ ?

3

Define $f(x) = \frac{1}{2}x^{2}- 8x - 17$ , restricting the domain of the function to $\left [ 0, \infty \right )$ .

Determine $f^{-1} (x)$ (you need not determine its domain restriction).

4

Define a function $f(x) = x^{2} + 9 x -17$ .

It is desired that is domain be restricted so that have an inverse. Which of these domain restrictions would not achieve that goal?

5

Given the relation below, identify the domain of the inverse of the relation.

$\left {(1, 2), (3, 4), (5, 6), (7, 8){ \right }$

6

If $f(x)=\frac{x}{x-3}$ , then which of the following is equal to $f^{-1}(x)$ ?

7

Define $f(x) = x^{2}- 4x - 4$ , restricting the domain of the function to $\left ( -\infty , 0 \right ]$ .

Determine $f^{-1} (x)$ (you need not determine its domain restriction).

8

Which of the following values of x is not in the domain of the function y = (2_x –_ 1) / (x_2 – 6_x + 9) ?

9

Given the relation below:

{(1, 2), (3, 4), (5, 6), (7, 8)}

Find the range of the inverse of the relation.

10

If $f(x) = x - 3$ , then find $f^{-1}(x)$

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