# What is the domain and range of #f(x)= (x+7)/(2x-8)#?

##### 2 Answers

Domain:

Range

#### Explanation:

**Disclaimer** : My explanation may be missing some certain aspects due to the fact that I am not a professional mathematician.

You can find both the Domain and Range by graphing the function and seeing when the function is not possible. This may be a trial and error and take some time to do.

You can also try the methods below

**Domain**

The domain would be all the values of

When

**Range**

To find the range, you can find the domain of the inverse function, to do this, rearrange the function to get x by itself. That would get quite tricky.

or

We can find the range by finding the value of y for which

As

The

Hence the function is not possible for when

A short way to do this is to get rid of everything except for the constants for the variables (the numbers in front of the

Hope that's helped.

#### Explanation:

#"y = f(x) is defined for all real values of x, except for any"#

#"that make the denominator equal zero"#

#"equating the denominator to zero and solving gives"#

#"the value that x cannot be"#

#"solve " 2x-8=0rArrx=4larrcolor(red)" excluded value"#

#"domain is " x inRR,x!=4#

#"to find any excluded values in the range, rearrange"#

#"f(x) making x the subject"#

#rArry(2x-8)=x+7larrcolor(blue)" cross-multiplying"#

#rArr2xy-8y=x+7#

#rArr2xy-x=7+8y#

#rArrx(2y-1)=7+8y#

#rArrx=(7+8y)/(2y-1)#

#"the denominator cannot equal zero"#

#"solve " 2y-1=0rArry=1/2larrcolor(red)" excluded value"#

#"range is " y inRR,y!=1/2#