# Precalculus : Relations and Functions

## Example Questions

### Example Question #51 : Pre Calculus

What is the domain of the following function?

-

Explanation:

The denominator becomes zero whenever cos(x) becomes -1 and this happens when x is an odd multiple of .  To avoid division by zero, we exclude all these numbers. Therefore the domain is:

### Example Question #1 : Evaluate Functions

Given  and , evaluate .

Explanation:

We are given two functions and asked to find f(h(7)).

I would begin by finding h(7)

Now that we know h(7), we go ahead and plug it into f(x).

So our final answer is simply 8.

### Example Question #2 : Evaluate Functions

Solve the function.

Explanation:

Determine the domain of .

Multiply  on both sides of the equation to cancel the denominator and divide the equation  by ten.

Since the domain states that , the only possible answer is .

### Example Question #3 : Evaluate Functions

Solve for :

Explanation:

Rewrite  so that the exponential variable is isolated.

Reconvert  to a similar base.  Use exponents to redefine the terms.

Since all terms are of the same base, use the property of log to eliminate the base on both sides of the equation.

Solve for .

### Example Question #4 : Evaluate Functions

Evaluate the following function when

Explanation:

Evaluate the following function when

To evaluate this function, simply plug-in 6 for t and simplify:

### Example Question #5 : Evaluate Functions

Determine the value of  of the function

Explanation:

In order to determine the value of  of the function we set  The value becomes

As such

### Example Question #6 : Evaluate Functions

Find the difference quotient of the function .

Explanation:

Difference quotient equation is

and

.

Now plug in the appropriate terms into the equation and simplify:

### Example Question #7 : Evaluate Functions

Find the value of the following function when

The function is undefined at

The function is undefined at

Explanation:

Find the value of the following function when

To evaluate this function, plug in 2 for x everywhere it arises and simplify:

So our answer must be undefined, because we cannot divide by

### Example Question #8 : Evaluate Functions

Find the value of  when

Explanation:

Find the value of  when

To evaluate this expression, plug in the given value of  everywhere you see a  and simplify:

If , what is ?