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Find the domain of the function

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

User Sparkles
by
8.5k points

1 Answer

14 votes

Answer:

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)

User Annoyingmouse
by
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