Mathematics, 19.04.2021 22:50 bryantjennifer1966

Find the inverse of each function

1. f(x) = 4/(x+2) - 2

2. f(x)= -2x^5 - 3

Answers: 3

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Answer from: 719729

We are given the following function:

f(x) = 4/(x+2) - 2

We are asked to determine the inverse of this function. To do that we will first change the "f(x)" for "y":

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

Now we will switch "x" and "y", like this:

$x = \frac{4}{x + 2} - 2$

Now we will solve for "y", first by adding 2 to both sides:

$x + 2 = \frac{4}{y + 2}$

Now we multiply both sides by "y+2":

(y + 2)(x + 2) = 4

Now we divide both sides by "x+2":

$y + 2 = \frac{4}{x + 2}$

Now we subtract 2 to both sides:

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

Now we change "y" for the inverse of f(x), that is:

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

And thus we found the inverse. A similar procedure can be used for function 2.

Answer from: 128585

9514 1404 393

1. f^-1(x) = 4/(x+2) -2

2. f^-1(x) = (-(x+3)/2)^(1/5)

Step-by-step explanation:

1. As with all "inverse function" problems, solve for y:

x = f(y)

x +2 = 4/(y +2) . . . . add 2

y +2 = 4/(x +2) . . . . . multiply by (y+2)/(x+2)

y = 4/(x+2) -2 . . . . . subtract 2

We see that this function is its own inverse. The attached graph shows it is symmetrical about the line y=x.

f^-1(x) = 4/(x+2) -2

2. x = f(y)

x +3 = -2y^5 . . . . add 3

-(x +3)/2 = y^5 . . . . . divide by 2

(-(x +3)/2)^(1/5) = y . . . . take the 5th root

f^-1(x) = (-(x +3)/2)^(1/5)

In typeset form, that is ...

$\displaystyle f^{-1}(x)=\sqrt[5]{\frac{-(x+3)}{2}}\\\\\text{or}\\\\f^{-1}(x)=-\frac{1}{2}\sqrt[5]{16x +48}$

This last version is with the denominator "rationalized" and the contents of the radical "simplified." It may be a preferred form.

_____

The graphs show the function and inverse are symmetrical about the line y=x, as they should be.

Find the inverse of each function
1. f(x) = 4/(x+2) - 2
2. f(x)= -2x^5 - 3

Answer from: Quest

0.84 dang lotta people are looking for this lol or if you round up its 1 but the overall answer to that is 0.84

step-by-step explanation:

Answer from: Quest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.