Question

F(x)=x-3/x+2 determine for each x-value where it is in the domain of f or not

-2 yes/no
0 yes/no
3 yes/no

PLS

Answer 1

f(x) = (x - 3)/(x + 2)

As the equation is basically a fraction the only thing that can be out of domain is if the denominator is equal to 0, so let's see when the denominator can be 0

x + 2 = 0

x = -2

So -2 is out of domain and all the other numbers are inside the domain.

Answer 2

`-2 \implies \sf no`

`0 \implies \sf yes`

`3 \implies \sf yes`

Explanation:

Given rational function:

`f(x)=(x-3)/(x+2)`

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

A rational function is not defined when its denominator is zero.

Therefore, to find when the given function f(x) is not defined, set the denominator to zero and solve for x:

`x+2=0 \implies x=-2`

Therefore, the domain is restricted to all values of x except x = -2.

This means that the domain of f(x) is (-∞, 2) ∪ (2, ∞).

In conclusion:

• x = -2 is not in the domain of f(x).
• x = 0 is in the domain of f(x).
• x = 3 is in the domain of f(x).