# Answers to Matched Problems in Domain and Range

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

## Matched Problems with Answers

### 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.

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