If c(x)= 5/x-2 and d(x) = x + 3, what is the domain of (cd)(x)?

1 answer:

3 0

$(fg)(x)=f(x)\cdot g(x)\\\\\text{We have}\ c(x)=\dfrac{5}{x-2}\ \text{and}\ d(x)=x+3.\ \text{Substitute}\\\\(cd)(x)=\dfrac{5}{x-2}\cdot(x+3)=\dfrac{5(x+3)}{x-2}\\\\\text{Domain:}\\\\\text{The denominator must be different than zero. Therefore}\\\\x-2\neq0\to x\neq2\\\\Answer:\ \text{Domain is the set of all real numbers except 2}\to D=\mathbb{R}-\{2\}$

You might be interested in

A swimming pool had 2.5 liters of water in it. Some water evaporated, and then the pool only had 2 million liters of water in it

djyliett [7]

Hi!

If I have done this correctly, then the answer is:

2 million is 80% of 2.5

That means that 20% of the water evaported.

5 0

3 years ago

A sphere has a diameter of 4 x 10^-3 mm. What is the approximate volume of the sphere? Use 3.14 for pi.

kolezko [41]

Answer:

$3.349 \times {10}^{ - 10} \: {mm}^{3}$

Step-by-step explanation:

$d = 4 \times {10}^{ - 3} \: mm \\ r = 2 \times {10}^{ - 3} \: mm \\ V_{sphere} = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \times 3.14 \times {(2 \times {10}^{ - 3} )}^{3} \\ = \frac{4}{3} \times 3.14 \times 8\times {10}^{ - 9} \\ = \frac{100.48}{3} \times {10}^{ - 9} \\ = 33.4933333\times {10}^{ - 9} \\ = 33.49 \times {10}^{ - 9} \\ = 3.349 \times {10}^{ - 10} \: {mm}^{3}$