All categories

3 years ago

Which function below is the inverse of f(x) = x2 − 25?

Mathematics

2 answers:

FrozenT [24]3 years ago

8 0

(x-5)(x+5) is the answer

IRINA_888 [86]3 years ago

3 0

$f(x) = x^{2} - 25
$ can be written as $y = x^{2} - 25$

when finding inverse the first step is to interchange x and y in the equation

∴ $(x) = (y)^{2} - 25$

then you simply solve for y

$x + 25 = y^{2}$

$y = \sqrt{ (x + 25)}$

Thus $f^{-1} (x) = \sqrt{(x + 25)}$

You might be interested in

A 75-gallon tank is filled with brine (water nearly saturated with salt; used as a preservative) holding 11 pounds of salt in so

Debora [2.8K]

Let $A(t)$ = amount of salt (in pounds) in the tank at time $t$ (in minutes). Then $A(0) = 11$ .

Salt flows in at a rate

$\left(0.6\dfrac{\rm lb}{\rm gal}\right) \left(3\dfrac{\rm gal}{\rm min}\right) = \dfrac95 \dfrac{\rm lb}{\rm min}$

and flows out at a rate

$\left(\dfrac{A(t)\,\rm lb}{75\,\rm gal + \left(3\frac{\rm gal}{\rm min} - 3.25\frac{\rm gal}{\rm min}\right)t}\right) \left(3.25\dfrac{\rm gal}{\rm min}\right) = \dfrac{13A(t)}{300-t} \dfrac{\rm lb}{\rm min}$

where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.

Then the net rate of salt flow is given by the differential equation

$\dfrac{dA}{dt} = \dfrac95 - \dfrac{13A}{300-t}$

which I'll solve with the integrating factor method.

$\dfrac{dA}{dt} + \dfrac{13}{300-t} A = \dfrac95$

$-\dfrac1{(300-t)^{13}} \dfrac{dA}{dt} - \dfrac{13}{(300-t)^{14}} A = -\dfrac9{5(300-t)^{13}}$

$\dfrac d{dt} \left(-\dfrac1{(300-t)^{13}} A\right) = -\dfrac9{5(300-t)^{13}}$

Integrate both sides. By the fundamental theorem of calculus,

$\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac1{(300-t)^{13}} A\bigg|_{t=0} - \frac95 \int_0^t \frac{du}{(300-u)^{13}}$

$\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac{11}{300^{13}} - \frac95 \times \dfrac1{12} \left(\frac1{(300-t)^{12}} - \frac1{300^{12}}\right)$

$\displaystyle -\dfrac1{(300-t)^{13}} A = \dfrac{34}{300^{13}} - \frac3{20}\frac1{(300-t)^{12}}$

$\displaystyle A = \frac3{20} (300-t) - \dfrac{34}{300^{13}}(300-t)^{13}$

$\displaystyle A = 45 \left(1 - \frac t{300}\right) - 34 \left(1 - \frac t{300}\right)^{13}$

After 1 hour = 60 minutes, the tank will contain

$A(60) = 45 \left(1 - \dfrac {60}{300}\right) - 34 \left(1 - \dfrac {60}{300}\right)^{13} = 45\left(\dfrac45\right) - 34 \left(\dfrac45\right)^{13} \approx 34.131$

pounds of salt.

7 0

1 year ago

What is 3X minus 6 and how did you get there??? A. 7 B. 9 C. 15 D. 18

Brilliant_brown [7]

Multiply 3x by -6, it gives you -18 so I'm going to say D

7 0

3 years ago

Read 2 more answers

Lydia makes $7,000 per month in New York City at her interior design company. She can't spend more than 25% of her income on the

Nataly [62]

Answer:

The maximum amount that Lydia can spend on a one-bedroom apartment is $ 1,750.

Step-by-step explanation:

Given that Lydia makes $ 7,000 per month in New York City at her interior design company, and that she can't spend more than 25% of her income on the one bedroom apartment, to determine the maximum amount of money that she can spend must be made the following calculation:

7,000 x 0.25 = X

1,750 = X

Thus, the maximum amount that Lydia can spend on a one-bedroom apartment is $ 1,750.

7 0

3 years ago

310-49what does 310 - 49 equal

enot [183]

Really,
$310 - 49 = 261$

Simple Calculator Calculation

6 0

2 years ago

Read 2 more answers

Which function family are these 3? thanks..

Julli [10]

Answer:

1) Function; Linear Function (y=x)

2) Function; Exponential Function (y=bˣ)

3) Not a function.

Step-by-step explanation:

So, let's go through each table of values. I'm also going to graph them (see attached graphs) because it will make things simpler and provide a visual.

First, also recall what the definition of a function is. A function is a function if and only if an x only has one distinct y-value. No x can have two or more y-values. For instance, (1,2) and (1,3) is not a function between the x repeats. So, let's go through the choices:

We have the table as shown. Let's plot the points. See TABLE 1:

First, there are no repeating x-values, so we can be sure that this is indeed a function.

Looking at the graph, we can see that this resembles a linear graph. So, the parent function of this is a line.

The parent function of a line is:

$y=x$

So, table 1 is associated with a linear function.

Let's again plot the points. See TABLE 2.

Again, there are no repeating x-values, so this is also a function.

Looking at the graph, this resembles an exponential function. The function increases slowly at first but starts increasing increasingly fast. The parent function is thus an exponential function.

So, table 2 is associated with an exponential function.

First, notice how all the x-coordinates are repeating. And since they do not equal the same thing, this is not a function.

Table 3 is not a function and so has no corresponding family function.

7 0

3 years ago

Read 2 more answers