Question

Find the domain of fg.

Answer 1

All real numbers

Explanation:

They ask us to find the domain of (fg)

f(x) = x+2

g(x) = ( 1 / x + 2 )

Multiplying these two equations, we get:

y = 1. And this equation is a straight line passing through 1 on the y-axis.

This means, the domain is all the real numbers.

Answer 2

Domain is all real number except
`-2`

Explanation:

`f(x)= x+2` and
`g(x)= (1)/(x+2)`

now we find fg

`fg= f(x) * g(x)`

Replace f(x) and g(x)

`f(x) * g(x)= (x+2)*(1)/(x+2)`

`f(x) * g(x)=(x+2)/(x+2)`

We have x+2 at the top and bottom. cancel it out

So we have hole at x+2

set the denominator =0 and solve for x

`x+2=0`

Subtract 2 on both sides

`x=-2`

the value of x cannot be
`-2`

Domain is all real number except
`-2`