# Answers to Matched Problems in Domain and Range

The answers to the matched problems in Domain and Range of a Function are presented.

### Matched Problem 1

Find the domain of function $$f$$ defined by
$$f(x) = -\dfrac{1}{x + 3}$$
Answer: The domain of function $$f$$ is the set of all values of $$x$$ in the interval
$$(-\infty, -3) \cup (-3, +\infty)$$

### Matched Problem 2

Find the domain of function $$f$$ defined by:
$$f(x) = \sqrt{-x + 9}$$
Answer: The domain of function $$f$$ is the set of all values of $$x$$ in the interval
$$(-\infty, 9]$$

### Matched Problem 3

Find the domain of function $$f$$ defined by:
$$f(x) = \dfrac{\sqrt{-x + 2}}{(x + 1)(x + 9)}$$
Answer: The domain of function $$f$$ is the set of all values of $$x$$ in the interval
$$(-\infty, -9) \cup (-9, -1) \cup (-1, 2]$$

### Matched Problem 4

Find the range of function $$f$$ defined by:
$$f(x) = x^2 + 3$$
Answer: The range of function $$f$$ is the set of all values of $$f(x)$$ in the interval
$$[3, +\infty)$$
More on Finding Domain and Range of Functions.