Question

What is the domain and range of `F(x) = 7/(6x-5)`?

Answer 1

Domain: `x inRR, x!=5/6`
Range: `F(x)in RR, F(x)!=0`

Explanation:

`F(x) = 7/(6x-5)` is not defined if `(6x-5)=0` (i.e. if `x=5/6`

therefore `x=5/6` must be excluded from the Domain

Consider the partial inverse equation:
`F(x) = 7/(6x-5)`
`rarr 6x-5 = 7/F(x)`

This will not be defined if `(F(x)=0`
therefore `F(x) =0` must be excluded from the range.
graph{7/(6x-5) [-20.27, 20.26, -10.13, 10.15]}