Find the domain for each function?

Question

1. g(x)= x/ x^2-16

2. G(x) = x+4/x^3-4x

3. G(x)= sqrt (1-x)

Answer 1

1) The rational function

We know that all possible values of x  is domain of a function.

A rational function is simply fraction and in a fraction the denominator cannot be equal to 0 because it would be undefined.

To find which number make the fraction undefined create an equation where the denominator is not equal to zero.

So the domain of the function all real numbers except -4 and 4.

Domain set

2) The rational function

To find which number make the fraction undefined create an equation where the denominator is not equal to zero.

So the domain of the function all real numbers except 0, - 2 and 2.

Domain set

3) The radical function

Step - 1

The index of radical function = 2

Step - 2

If the index is even number set the expression in the radical equals to greater than or equal to 0.

1 - x  ≥ 0

Step - 3

Solve the above inequality.

1 - x  ≥ 0

x  ≤ 1

The domain of is { x ∈ R : x ≤ 1 }.