Question

Find the domain of the function f, defined by f(x)=√((x^3)(9-x))

Answer 1

Answer on Question #75836 – Math – Calculus

Question

Find the domain of the function $f$, defined by $f(x) = \sqrt{\bigl((x^3)(9 - x)\bigr)}$

Solution

$$x^3(9 - x) \geq 0$$

Dividing by $x^2 \geq 0$

$$x(9 - x) \geq 0$$

Multiplying by (-1)

$$x(x - 9) \leq 0$$

The table of signs

It follows from the table of signs that the solution of the inequality $x(x - 9) \leq 0$ is $0 \leq x \leq 9$.

The domain of the function $f$ is given by

$$D(f) = [0, 9].$$

Answer: $D(f) = [0, 9]$.

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