### All Precalculus Resources

## Example Questions

### Example Question #1 : Evaluate Functions

Given and , evaluate .

**Possible Answers:**

**Correct answer:**

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.

**Possible Answers:**

**Correct answer:**

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 :

**Possible Answers:**

**Correct answer:**

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

**Possible Answers:**

**Correct answer:**

Evaluate the following function when

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

So our answer is:

### Example Question #5 : Evaluate Functions

Determine the value of of the function

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

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

**Possible Answers:**

The function is undefined at

**Correct answer:**

The function is undefined at

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

**Possible Answers:**

**Correct answer:**

Find the value of when

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

So our answer is:

### Example Question #9 : Evaluate Functions

If , what is ?

**Possible Answers:**

**Correct answer:**

In order to evaluate this function, simply substitute the value of as a replacement of .

Simplify using the order of operations.

The answer is:

### Example Question #10 : Evaluate Functions

Evaluate for .

**Possible Answers:**

**Correct answer:**

We evaluate the function when .

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