Answer:
The domain of f is (-∞,4)
Step-by-step 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
[tex]f(x)=\frac{1}{\sqrt{4-x} }[/tex]
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)
