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3 years ago

Find the inverse function g(x) of the function f(x)=2x+1

Mathematics

1 answer:

choli [55]3 years ago

6 0

Answer:

The inverse function is f(x) = (x - 1)/2

Step-by-step explanation:

To find the inverse of any function, start by switching the x and f(x) values.

f(x) = 2x + 1

x = 2f(x) + 1

Now solve for the new f(x). The result will be your inverse function.

x = 2f(x) + 1

x - 1 = 2f(x)

(x - 1)/2 = f(x)

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Several terms of a sequence {an}n=1 infinity are given. A. Find the next two terms of the sequence. B. Find a recurrence relatio

s344n2d4d5 [400]

Answer:

A) $\frac{1}{1024},\frac{1}{4096}$

B) $\left\{\begin{matrix}a(1)=1 & \\ a(n)=a(n-1)*\frac{1}{4} &\:for\:n=1,2,3,4,... \end{matrix}\right.$

C) $\\a_{n}=nq^{n-1} \:for\:n=1,2,3,4,...$

Step-by-step explanation:

1) Incomplete question. So completing the several terms: $\left \{a_{n}\right \}_{n=1}^{\infty}=\left \{ 1,\frac{1}{4},\frac{1}{16},\frac{1}{64},\frac{1}{256},... \right \}$

We can realize this a Geometric sequence, with the ratio equal to:

$q=\frac{1}{4}$

A) To find the next two terms of this sequence, simply follow multiplying the 5th term by the ratio (q):

$\frac{1}{256}*\mathbf{\frac{1}{4}}=\frac{1}{1024}\\\\\frac{1}{1024}*\mathbf{\frac{1}{4}}=\frac{1}{4096}\\\\\left \{ 1,\frac{1}{4},\frac{1}{16},\frac{1}{64},\frac{1}{256},\mathbf{\frac{1}{1024},\frac{1}{4096}}\right \}$

B) To find a recurrence a relation, is to write it a function based on the last value. So that, the function relates to the last value.

$\left\{\begin{matrix}a(1)=1 & \\ a(n)=a(n-1)*\frac{1}{4} &\:for\:n=1,2,3,4,... \end{matrix}\right.$

C) The explicit formula, is one valid for any value since we have the first one to find any term of the Geometric Sequence, therefore:

$\\a_{n}=nq^{n-1} \:for\:n=1,2,3,4,...$

6 0

3 years ago

1.5 3.9 6.3 8.7 what is the sequence term

Korolek [52]

Answer: 1.9

Step-by-step explanation:

because you keep adding 1.9 to get your result

7 0

3 years ago

Read 2 more answers

Alan, Bill, and Calvin are playing a game with collectible cards. At the moment, Alan has 11 less than 2 1/2 times the number of

kramer

Bill has 12 cards. I figured this out by making a table and drawing an equation:

7 0

3 years ago

In a sample of 60 electric motors, the average efficiency (in percent) was 85 and the standard deviation was 2. Section 05.01 Ex

jasenka [17]

Answer:

95% confidence interval for the mean efficiency is [84.483 , 85.517].

Step-by-step explanation:

We are given that in a sample of 60 electric motors, the average efficiency (in percent) was 85 and the standard deviation was 2.

So, the pivotal quantity for 95% confidence interval for the population mean efficiency is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\mu$ = sample average efficiency = 85

$\sigma$ = sample standard deviation = 2

n = sample of motors = 60

$\mu$ = population mean efficiency

So, 95% confidence interval for the mean efficiency, $\mu$ is ;

P(-2.0009 < $t_5_9$ < 2.0009) = 0.95

P(-2.0009 < $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ < 2.0009 ) = 0.95

P( $-2.0009 \times {\frac{s}{\sqrt{n} }$ < ${\bar X - \mu}$ < $2.0009 \times {\frac{s}{\sqrt{n} }$ ) = 0.95

P( $\bar X -2.0009 \times {\frac{s}{\sqrt{n} }$ < $\mu$ < $\bar X +2.0009 \times {\frac{s}{\sqrt{n} }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X -2.0009 \times {\frac{s}{\sqrt{n} }$ , $\bar X +2.0009 \times {\frac{s}{\sqrt{n} }$ ]

= [ $85 -2.0009 \times {\frac{2}{\sqrt{60} }$ , $85 +2.0009 \times {\frac{2}{\sqrt{60} }$ ]

= [84.483 , 85.517]

Therefore, 95% confidence interval for the population mean efficiency is [84.483 , 85.517].

8 0

3 years ago

Use the information given to enter an equation in standard form.

sladkih [1.3K]

X1,y1 and x2,y2 are on the line

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3 years ago