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Bess [88]
3 years ago
15

Write g(x) so that it is the inverse of the given function f(x). f(x) = 1/3x - 5/3 g(x) =

Mathematics
1 answer:
jolli1 [7]3 years ago
6 0

9514 1404 393

Answer:

  g(x) = 3x +5

Step-by-step explanation:

The inverse function can be found by solving ...

  x = f(y)

  x = 1/3y -5/3 . . . . . use the definition of f(x)

  3x = y -5 . . . . . . . . multiply by 3

  3x +5 = y . . . . . . . .add 5

Then the inverse function is ...

  g(x) = 3x +5

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Solve for x. <br><br> x + 3x + 5 =21
timurjin [86]

Answer:

x=4

Step-by-step explanation:

In order to solve for x, we must isolate x on one side of the equation.

x+3x+5=21

First, combine like terms. x and 3x are both terms with variables, and can be combined.

(x+3x) + 5=21

4x + 5=21

5 is being added to 4x. The inverse of addition is subtraction. Subtract 5 from both sides of the equation.

4x+5-5= 21-5

4x= 16

x is being multiplied by 4. The inverse of multiplication is division. Divide both sides by 4.

4x/4=16/4

x= 16/4

x=4

Let's check our solution. Plug 4 in for x and solve.

x+3x+5=21

4+3(4)+5=21

4+12+5=21

16+5=21

21=21

This solution checks out, so we know our answer is correct.

x is equal to 4, x=4.

4 0
3 years ago
Read 2 more answers
A sociologist develops a test to measure attitudes towards public transportation, and 27 randomly selected subjects are given th
taurus [48]

Answer:

The margin of error for the 95% confidence interval for the mean score of all such subjects is of 8.45.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 27 - 1 = 26

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 26 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.95}{2} = 0.975. So we have T = 2.0518

The margin of error is:

M = T\frac{s}{\sqrt{n}}

In which s is the standard deviation of the sample and n is the size of the sample.

In this question:

n = 27, s = 21.4. So

M = 2.0518\frac{21.4}{\sqrt{27}}

M = 8.45

The margin of error for the 95% confidence interval for the mean score of all such subjects is of 8.45.

5 0
3 years ago
Between x=2 and x=3, which function has a greater average rate of change than f(x)=2^x has?
maxonik [38]

Answer: f(3)

Step-by-step explanation:

First find the formula for the rate of change by taking the derivative of 2^x. Let f(x) equal some hypothetical y-value, then take the natural log of both sides.

y=2^x\\\ln(y)=x \ln(2)

Implicitly differentiate the left side and take the derivative of the right side

\frac{y'}{y} =\ln(2)

Multiply both sides by 'y' which was defined as 2^x

y'=\ln(2)*2^x

Plug in x = 2 and x = 3 to see which slope is larger

y'=\ln(2)*2^2=4\ln(2)\\y'=\ln(2)*2^3=8\ln(2)

4 0
3 years ago
Simplify fully 16x÷2xy
kogti [31]

Answer:

so you divide 16x÷2xy=8/y

which also same as 8y-¹

8 0
2 years ago
Read 2 more answers
Robbie had p coins. Then he found 59 more coins in a drawer. Choose the expression that shows how many coins Robbie has now.
attashe74 [19]

Answer:

y=p+59

Step-by-step explanation:

3 0
3 years ago
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