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

Practice Questions

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

Questions

6

1

Define function as follows:

$f(x) = \cos \frac{x}{2}$

On which of the following restrictions of the domain of would $f^{-1}$ not exist?

2

Define function as follows:

$f(x) = \sin\left ( \frac{x}{2}+ \frac{\pi }{3} \right )$

Suppose the domain of were to be restricted so that could have an inverse. Which of the following restrictions would not give an inverse?

3

Define function as follows:

$f(x) = x^{3} + 6 x$

In which of the following ways could the domain of be restricted so that does not have an inverse?

4

Consider the following statement to be true:

If a fish is a carnivore, then it is a shark.

Which of the following statements must also be true?

5

Define function as follows:

$f(x) = x^{3} -7 x$

Suppose the domain of were to be restricted so that could have an inverse. Which of the following restrictions would not give an inverse?

6

Define function as follows:

$f(x) = x^{2} + x - 6$

On which of the following restrictions of the domain of would $f^{-1}$ not exist?

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