Question

What is the domain and range of `g(x) = (7x+4)/(x+4)`?

Answer 1

The domain is `x in (-oo, -4)uu (-4, +oo)`.
The range is `y in (-oo, 7) uu (7, +oo)`

Explanation:

Let `y=(7x+4)/(x+4)`

The denominator is `!=0`

Therefore,

`x+4!=0`

`x!=-4`

The domain is `x in (-oo, -4)uu (-4, +oo)`

Also,

`y(x+4)=7x+4`

`yx+4y=7x+4`

`yx-7x=4-4y`

`x(y-7)=(4-4y)`

`x=(4-4y)/(y-7)`

The denominator is `!=0`

Therefore

`y-7!=0`

`y!=7`

The range is `y in (-oo, 7) uu (7, +oo)`

graph{(y-((7x+4)/(x+4)))(y-7)=0 [-36.53, 36.52, -18.28, 18.27]}