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Find domain for f(x)=- sqrt 5-x-3

Find domain for f(x)=- sqrt 5-x-3-example-1

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Final answer:

The domain of the function f(x) = -√(5 - x) - 3 is all real numbers less than or equal to 5, which is expressed as (-∞, 5].

Step-by-step explanation:

To find the domain of the function f(x) = -√(5 - x) - 3, we must identify all the values of x for which the function is defined.

The square root function is only defined for non-negative numbers.

Therefore, the expression inside the square root, 5 - x, must be greater than or equal to zero.

To find these values, we set up the inequality 5 - x ≥ 0.

Solving for x, we get x ≤ 5.

This means that x can be any real number up to and including 5.

So, the domain of the function is (-∞, 5].

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