Inputing Values into a Function

🏆Practice domain of a function

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 X=3

Y=2 Y=2

Z=? Z=\text{?}

X2+Y=Z X^2+Y=Z

32+2=11 3^2+2=11

Answer: Z=11 Z=11

X Y Z By assigning the numerical value, the general form becomes a particular case

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

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Test yourself on domain of a function!

einstein

Given the following function:

\( \frac{5-x}{2-x} \)

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

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Examples and exercises with solutions for assigning numerical value in a function

Exercise #1

Given the following function:

9x4 \frac{9x}{4}

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

Video Solution

Step-by-Step Solution

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

Answer

No, the entire domain

Exercise #2

Given the following function:

65(2x2)2 \frac{65}{(2x-2)^2}

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

Video Solution

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:

(2x2)20 (2x-2)^2\ne0

2x2 2x\ne2

x1 x\ne1

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

Answer

Yes, x1 x\ne1

Exercise #3

Given the following function:

5+4x2+x2 \frac{5+4x}{2+x^2}

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

Video Solution

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.

Answer

No, the entire domain

Exercise #4

Given the following function:

5x2x \frac{5-x}{2-x}

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

Video Solution

Answer

Yes, x2 x\ne2

Exercise #5

Given the following function:

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

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

Video Solution

Answer

Yes, x4 x\ne-4

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