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3 years ago

Find the inverse of f(x)=(x−5)/(−4x−2)

Mathematics

1 answer:

uysha [10]3 years ago

7 0

Answer:

${f}^{ - 1} (x)= \frac{ 5 - 2x }{ 4x + 1}$

Step-by-step explanation:

The given rational function is

$f(x) = \frac{x - 5}{ - 4x - 2}$

Let

$y = \frac{x - 5}{ - 4x - 2}$

Interchange x and y

$x= \frac{y- 5}{ - 4y - 2}$

Cross multiply

$x( - 4y - 2)= y- 5$

Expand

$- 4xy - 2x= y- 5 \\ - 4xy - y= 2x - 5 \\y( - 4x - 1)= 2x - 5$

Solve for y;

$y= \frac{ 2x - 5}{ - 4x - 1}$

$y= \frac{ 5 - 2x }{ 4x + 1}$

Therefore

${f}^{ - 1} (x)= \frac{ 5 - 2x }{ 4x + 1}$

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2 years ago

Read 2 more answers

For what value(s) of k will the relation not be a function

skelet666 [1.2K]

We are given two relations

(a)

Relation (R)

$R=[((k-8.3+2.4k),-5),(-\frac{3}{4}k,4)]$

We know that

any relation can not be function when their inputs are same

so, we can set both x-values equal

and then we can solve for k

$k-8.3+2.4k=-\frac{3}{4} k$

$3.4k-8.3=-\frac{3}{4}k$

$3.4k\cdot \:10-8.3\cdot \:10=-\frac{3}{4}k\cdot \:10$

$4k-83=-\frac{15}{2}k$

$34k=-\frac{15}{2}k+83$

$\frac{83}{2}k=83$

$83k=166$

$k=2$ ............Answer

(b)

S = {(2−|k+1| , 4), (−6, 7)}

We know that

any relation can not be function when their inputs are same

so, we can set both x-values equal

and then we can solve for k

$2-|k+1|=-6$

$2-\left|k+1\right|-2=-6-2$

$-\left|k+1\right|=-8$

$\left|k+1\right|=8$

Since, this is absolute function

so, we can break it into two parts

$|f\left(k\right)|=a\quad \Rightarrow \:f\left(k\right)=-a\quad \mathrm{or}\quad \:f\left(k\right)=a$

$k+1=-8\quad \quad \mathrm{or}\quad \:\quad \:k+1=8$

we get

$k+1=-8\quad$

$k=-9$

$k+1=8\quad$

$k=7$

so,

$k=-9\quad \mathrm{or}\quad \:k=7$ ...............Answer

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3 years ago

Rewrite the equation in exponential form, and show how you got there:

Brut [27]

Answer: $13^0=1$

Step-by-step explanation:

Logarithms are in the format $log_{b} a=c$ while exponential form is in the format $b^c=a$

So we can transfer a,b, and c from the log form to the exponential form

$log_{13} 1=0\\\\13^0=1$

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2 years ago

The travel time on a section of a Long Island Expressway (LIE) is normally distributed with a mean of 80 seconds and a standard

user100 [1]

Answer:

The travel time that separates the top 2.5% of the travel times from the rest is of 91.76 seconds.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 80 seconds and a standard deviation of 6 seconds.

This means that $\mu = 80, \sigma = 6$