# Inputing Values into a Function - Examples, Exercises and Solutions

Generally, a numerical value is assigned in equations with variables or in mathematical expressions that include variables.

The assignment involves changing the variables in a mathematical expression or equation to specific numerical values.

For example

$X=3$

$Y=2$

$Z=\text{?}$

$X^2+Y=Z$

$3^2+2=11$

Answer: $Z=11$

By assigning the numerical value, the general form becomes a particular case.

## Examples with solutions for Inputing Values into a Function

### Exercise #1

Given the following function:

$\frac{9x}{4}$

Does the function have a domain? If so, what is it?

### Step-by-Step Solution

Since the function's denominator equals 4, the domain of the function is all real numbers, meaning all X.

No, the entire domain

### Exercise #2

Given the following function:

$\frac{65}{(2x-2)^2}$

Does the function have a domain? If so, what is it?

### Step-by-Step Solution

The denominator of the function cannot be equal to 0.

Therefore, we will set the denominator equal to 0 and solve for the domain:

$(2x-2)^2\ne0$

$2x\ne2$

$x\ne1$

In other words, the domain of the function is all numbers except 1.

Yes, $x\ne1$

### Exercise #3

Given the following function:

$\frac{5+4x}{2+x^2}$

Does the function have a domain? If so, what is it?

### Step-by-Step Solution

Since the denominator is positive for all X, the domain of the function is the entire domain.

That is, all X, therefore there is no domain restriction.

No, the entire domain

### Exercise #4

Given the following function:

$\frac{5-x}{2-x}$

Does the function have a domain? If so, what is it?

### Video Solution

Yes, $x\ne2$

### Exercise #5

Given the following function:

$\frac{49+2x}{x+4}$

Does the function have a domain? If so, what is it?

### Video Solution

Yes, $x\ne-4$

### Exercise #6

Given the following function:

$\frac{5}{x}$

Does the function have a domain? If so, what is it?

### Video Solution

Yes, $x\ne0$

### Exercise #7

Given the following function:

$\frac{23}{5x-2}$

Does the function have a domain? If so, what is it?

### Video Solution

Yes, $x\ne\frac{2}{5}$

### Exercise #8

Look at the following function:

$\frac{2x+20}{\sqrt{2x-10}}$

What is the domain of the function?

x > 5

### Exercise #9

Consider the following function:

$\frac{3x+4}{2x-1}$

What is the domain of the function?

### Video Solution

$x\ne\frac{1}{2}$

### Exercise #10

Look at the following function:

$\frac{2x+2}{3x-1}$

What is the domain of the function?

### Video Solution

$x\ne\frac{1}{3}$

### Exercise #11

Given the following function:

$\frac{12}{8x-4}$

What is the domain of the function?

### Video Solution

$x\ne\frac{1}{2}$

### Exercise #12

Look at the following function:

$\frac{5x+2}{4x-3}$

What is the domain of the function?

### Video Solution

$x\ne\frac{3}{4}$

### Exercise #13

Look at the following function:

$\frac{10x-3}{5x-3}$

What is the domain of the function?

### Video Solution

$x\ne\frac{3}{5}$

### Exercise #14

Look the following function:

$\frac{1}{5x-4}$

What is the domain of the function?

### Video Solution

$x\ne\frac{4}{5}$

### Exercise #15

Given the following function:

$\frac{24}{21x-7}$

What is the domain of the function?

### Video Solution

$x\ne\frac{1}{3}$