Functions Operations - A closer look at division.

Functions Operations

A Closer Look at Division.

By Melodie Hunt

Division:

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Notice that for division we say that the denominator can't equal zero.

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Why do we say that? What happens to a fraction when the denominator equals zero?​

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Let's see what happens in the next example.​

Multiple Choice

Evaluate f(9)

$$f\left(x\right)\ =\ \frac{x}{x-9}$$  

• 1

• 0

• 9

• Undefined

​As we saw when x equaled 9 the function was undefined. This means that x = 9 is not part of the domain of the function.

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If a question asks for the restricted domain, you would say:

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"The domain is all real number except x = 9."

OR ​you could simply say x ≠​ 9.

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If a question asks for the domain restriction, you would say:

"x=9"​

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Let's try some problems related to domain.​

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Multiple Choice

$$\frac{5}{x}$$  What is the restricted domain?

• $$x\ne5$$  

• $$x\ne0$$  

• $$x\ge5$$  

• $$x\ge0$$  

Multiple Choice

$$\frac{2x}{x}$$  Choose the domain for which the function is defined.

• $$x\ne2$$  

• $$x\ge2$$  

• $$x\ge0$$  

• $$x\ \ne\ 0$$  

Multiple Choice

$$\frac{3}{x+4}$$  What is the restricted domain?

• $$x\ge4$$  

• $$x\ge3$$  

• $$x\ne3$$  

• $$x\ne-4$$  

Multiple Choice

$$\frac{3}{x-6}$$  What is the excluded domain?

• $$x\ne6$$  

• $$x\ne3$$  

• $$x\ge3$$  

• $$x\ge6$$  

Multiple Choice

What are the domain restrictions of $$f\left(x\right)=\frac{x+3}{x^2-16}$$  ?

• $$x\ne4,-4$$  

• $$x\ne0$$  

• $$x\ge16$$  

• $$\left(-4,4\right)$$  

Multiple Choice

What is the domain restriction of $$f\left(x\right)=\frac{3}{2x+7}$$  ?

• $$x\ne\frac{7}{2}$$  

• $$x\ne-\frac{7}{2}$$  

• $$x\ne-7$$  

• $$x\ne7$$  

Multiple Choice

If f(x) = 3, and g(x) = x² + 6x + 5, what are the domain restrictions $$\frac{f}{g\ }\left(x\right)$$

• $$x\ne-5,-1$$  

• $$x\ne1,5$$  

• $$x>5,\ x<1$$  

• $$x<-5,\ x>-1$$  

Multiple Choice

Given the functions

$$f\left(x\right)=3x-9$$  and  $$g\left(x\right)=x-11$$   find  $$\frac{g}{f}$$  

• $$\frac{3x-9}{x-11}$$   $$x\ne11$$  

• $$\frac{x-11}{3x-9}$$  ,

  $$x\ne3$$  

• $$\frac{3x}{x}$$   $$x\ne0$$

• $$\frac{9}{11}$$