# How do you find the domain and range of #f(x) = 6/(x-4)#?

##### 2 Answers

see explanation.

#### Explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.

#"solve " x-4=0rArrx=4#

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

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

#y=6/(x-4)#

#rArry(x-4)=6#

#rArrxy-4y=6rArrxy=6+4y#

#rArrx=(6+4y)/y# To obtain the range apply same reasoning as used for domain.

#rArr"range is " y inRR,y!=0#

Domain:

Range:

#### Explanation:

Let us first deal with the domain. The domain of a function are all the values for which the function is defined. In your example, it is all the

In calculus courses, "unless stated otherwise" you want the domain to be as a large part of the real line (denoted

Let us continue with the range of the function. The range is the set of all the values that

For very small

Since

By similar reasoning, we can consider all

In total, we see that

The reason why

Trying to plot the function can give you an idea of the range and domain. But be warned, plotting tools sometimes do not show correct results, and rarely give you the whole picture.

graph{6/(x -4) [-35.75, 44.25, -20.12, 19.88]}