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3 years ago

Let f(x)=3x-6 and g(x)=x-2 find f(g(5))-ie. (f • g)(5) and its domain

Mathematics

1 answer:

Molodets [167]3 years ago

3 0

Solution for f(g(5)):

The notation f(g(5)) or (f • g)(5) means that we first plug 5 into the function g(x), simplify, then plug the answer that we got to f(x). We will do this step-by-step:

Step 1: Plugging 5 to g(x)

$g(5)=5-2=3$

Step 2: Plugging the answer to f(x)

$f(3)=3(3)-6=9-6=3$

ANSWER: f(g(5)) is equal to 3.

Domain:

For the function f(g(x)), we can find the domain by analyzing the domains of each individual functions separately and excluding certain values depending on the restrictions from the outermost function.

However, since both functions have all real numbers as its domain, we will not need to do any exclusion anymore.

ANSWER: The domain of the function is all real numbers.

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The tile along the edge of a triangular community pool needs to be replaced.

Gre4nikov [31]

Answer:

Third option: 12x^2+8x+25

Step-by-step explanation:

s1=8x^2

s2=4x^2+15

s3=8x+10

Total perimeter of the pool edge: P

P=s1+s2+s3

Replacing s1, s2 and s3 in the formula above:

P=(8x^2)+(4x^2+15)+(8x+10)

P=8x^2+4x^2+15+8x+10

Adding like terms:

P=12x^2+8x+25

6 0

2 years ago

Read 2 more answers

Sample size: A researcher is trying to decide how many people to survey. Which of the following sample sizes will result in a co

oksian1 [2.3K]

Answer:

Step-by-step explanation:

Given that a researcher is trying to decide how many people to survey.

We have confidence intervals are intervals with middle value as the mean and on either side margin of error.

Confidence interval = Mean ± Margin of error

Thus confidence interval width depends on margin of error.

Margin of error = $Critical value *\frac{\sigma}{\sqrt{n} }$

Thus for the same confidence level and std deviation we find margin of error is inversely proportional to square root of sample size.

Hence for small n we get wide intervals.

So if sample size = 300, the researcher will get wider confidence interval

4 0

3 years ago

There was 2/3 of pan of lasagna in the refrigerator. Bill and his friends ate half of what was left. Write a number sentence and

Veseljchak [2.6K]

Half of 2/3 is:

$\frac { 1 }{ 2 } \times \frac { 2 }{ 3 } =\frac { 1 }{ 3 }$

This means that 1/3 was left. This also means that they ate 1/3 of the lasagne.

Model diagram can be seen in attachment.