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3 years ago

Please Help Me Prove This

Mathematics

1 answer:

AURORKA [14]3 years ago

7 0

It depends on what the question is

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Can you please help me on me review?

maxonik [38]

Answer:

$(fg)(x) =8 \sqrt[6]{ (3 - x)^ {5 }}$

$(\frac{f}{g} )(x) = \frac{1}{2} \sqrt[6]{3 - x}$

$(fg)(2) = 8$

$(\frac{f}{g} )(2) =\frac{1}{2}$

The domain of (fg)(x) is all real numbers

The domain of (f/g)(x) is x>3

Step-by-step explanation:

The given functions are

$f(x) = 2 \sqrt{3 - x}$

and

$g(x) = 4 \sqrt[3]{3 - x}$

We want to to evaluate:

$(fg)(x) = f(x) \cdot \: g(x)$

$(fg)(x) =( 2 \sqrt{3 - x} )\times ( 4\sqrt[3]{3 - x} )$

We multiply to get:

$(fg)(x) =8(3 - x)^{ \frac{1}{2} } ( 3 - x)^{ \frac{1}{3} }$

$(fg)(x) =8(3 - x)^ {\frac{1}{2 } + \frac{1}{3}}$

$(fg)(x) =8(3 - x)^ {\frac{5}{6 } }$

$(fg)(x) =8 \sqrt[6]{ (3 - x)^ {5 }}$

The domain of (fg)(x) is all real numbers.

Similarly;

$(\frac{f}{g} )(x) = \frac{f(x)}{g(x)}$

$(\frac{f}{g} )(x) = \frac{2 \sqrt{3 - x} }{4 \sqrt[3]{3 - x} } = \frac{1}{2} \sqrt[6]{3 - x}$

The domain is all real numbers greater than 3.

We need to evaluate (fg)(2) and (f/g)(2) to get:

$(fg)(2) =8 \sqrt[6]{ (3 - 2)^ {5 }} = 8 \sqrt[6]{ {1}^{5} } = 8$

$(\frac{f}{g} )(2) = \frac{1}{2} \sqrt[6]{3 - 2} = \frac{1}{2}$

3 0

3 years ago

Yolo has 2 pieces of string. One is 32 inches long, the other is 48 inches long. She wants to make as many necklaces as she can,

Arte-miy333 [17]

The Greatest Common Factor of 32 and 48 is 16.

The longest necklace she can make is of 16 inches length.

3 0

3 years ago

Read 2 more answers

On a coordinate plane, 2 exponential functions are shown. f (x) decreases from quadrant 2 to quadrant 1 and approaches y = 0. It

aliina [53]

Answer: $-4\left(\frac{1}{2} \right)^{x}$

Step-by-step explanation:

To reflect the graph of a function across the x-axis,

$y=f(x) \longrightarrow y=-f(x)$

3 0

2 years ago

3.26d+9.75d-2.65= helppppppppppppppp

Crazy boy [7]

I’ll teach you how to solve 3.26d+9.75d-2.65
——————————————-
3.26d+9.75d-2.65
Collect like terms by adding their coefficients:
(3.26+9.75)d-2.65
Add the numbers:
3.26+9.75= 13.01
13.01d-2.65
Your Answer Is 13.01d-2.65
Plz mark me as brainliest if this helped :)

4 0

3 years ago

Given the exponential model y= 200(.80)^x, tell whether the model represents exponential growth or decay. Then, tell what the gr

BaLLatris [955]

This function represents exponential decay.

We know it's exponential because the value the base (200) is being multiplied by is being raised to the power of x.

In this case, the multiplication value is 0.8, which is less than 1.

If the multiplication value is less than 1, than the function will decay, rather than grow.

In this case, the factor is 0.8, or 80%.

4 0

3 years ago