### All Precalculus Resources

## Example Questions

### Example Question #10 : Evaluate Functions

Evaluate for .

**Possible Answers:**

**Correct answer:**

We evaluate the function when .

### Example Question #31 : Relations And Functions

Find the domain of f(x) below

**Possible Answers:**

**Correct answer:**

We have We have for all real numbers. when . The denominator is undefined when .

The nominator is defined if .

The domain is:

### Example Question #32 : Relations And Functions

The domain of the following function

is:

**Possible Answers:**

**Correct answer:**

is defined when . Since we do not want to be 0 in the denominator we must have . when x=2.

Thus we need to exclude 2 also. Therefore the domain is:

### Example Question #33 : Relations And Functions

Find the range of the following function:

**Possible Answers:**

**Correct answer:**

Every element of the domain has as image 7.This means that the function is constant . Therefore,

the range of f is :{7}.

### Example Question #34 : Relations And Functions

What is the domain of the following function:

**Possible Answers:**

**Correct answer:**

Note that in the denominator, we need to have to make the square root of x defined. In this case is never zero. Hence we have no issue when dividing by this number. Therefore the domain is the set of real numbers that are

### Example Question #35 : Relations And Functions

Find the domain of the following function f(x) given below:

**Possible Answers:**

**Correct answer:**

. Since for all real numbers. To make the square root positive we need to have .

Therefore the domain is :

### Example Question #36 : Relations And Functions

What is the range of :

**Possible Answers:**

**Correct answer:**

We know that . So .

Therefore:

.

This gives:

.

Therefore the range is:

### Example Question #37 : Relations And Functions

Find the range of f(x) given below:

**Possible Answers:**

**Correct answer:**

Note that: we can write f(x) as :

.

Since,

Therefore,

So the range is

### Example Question #38 : Relations And Functions

What is the range of :

**Possible Answers:**

**Correct answer:**

We have .

Adding 7 to both sides we have:

.

Therefore .

This means that the range of f is

### Example Question #39 : Relations And Functions

Find the domain of the following function:

**Possible Answers:**

**Correct answer:**

The part inside the square root must be positive. This means that we must be . Thus

. Adding -121 to both sides gives . Finally multiplying both sides by (-1) give:

with x reals. This gives the answer.

Note: When we divide by a negative we need to flip our sign.

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