Question

Find the domain of the function

f(x)=
`(1)/(√(4-x) )`
write your answer in interval notation.

Answer 1

The domain of f is (-∞,4)

Explanation:

Domain of a Function

The domain of a function f is the set of all the values that the input variable can take so the function exists.

We are given the function

`f(x)=(1)/(√(4-x) )`

It's a rational function which denominator cannot be 0. In the denominator, there is a square root whose radicand cannot be negative, that is, 4-x must be positive or zero, but the previous restriction takes out 0 from the domain, thus:

4 - x > 0

Subtracting 4:

- x > -4

Multiplying by -1 and swapping the inequality sign:

x < 4

Thus the domain of f is (-∞,4)