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erastova [34]
3 years ago
8

If f(x) and f -1 (x) are inverse functions of each other and f(x) = 2x+5, what is f -1 (8)?

Mathematics
1 answer:
Aleksandr [31]3 years ago
5 0

Answer: 3/2

Step-by-step explanation:

The first one: y=2x+5

X=2y+5.Then solve for y after switching x and y

X-5=2y, X-5/2=y

Since F-1= X-5/ 2, we plug the value of X in

8-5/2, so it should be 3/2

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If the slope is -2 and the y-intercept is -5, then the linear equation is y = -2x - 5.
Lisa [10]

Answer:

True

Step-by-step explanation:

y = mx + b,

where m = slope and b = y-intercept.

You have m = -2 and b = -5, so you get

y = -2x - 5

Answer: True

4 0
2 years ago
Pls help. This is due today!
JulijaS [17]

Answer:

goodluck

Step-by-step explanation:

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4 0
3 years ago
Examine this system of equations. Which numbers can be multiplied by each equation so that when the two equations are added toge
WARRIOR [948]

You can use the fact that when coefficient of x variable are of equal magnitude but opposite sign, then adding them will make the coefficient 0, thus, making the x variable eliminated.

The numbers that can be multiplied by each equation so that when the two equations are added together, the x term is eliminated is given by

Option A: –10 times the first equation and 3 times the second equation

<h3>How does elimination works?</h3>

This method is actually called method of elimination to solve a system of linear equations.

We make one specific variable's coefficients of equal magnitude so that we can subtract or add the equations and eliminate that variable to make it easy to get the value of the other variable which will then help in getting the value of the first variable (if working in dual variable system).

If we have equations:

a_1x + b_1y  = c_1\\a_2x + b_2y = c_2

then, if we want to eliminate variable x, then we have to multiply equation 1 with

- \dfrac{a_2}{a_1}

which will make coefficient of x in first equation as

a_1 \times - \dfrac{a_2}{a_1} = -a_1

Then adding both equation will eliminate the variable x.

We could've skipped that -ve sign and at then end, instead of adding, we could've subtracted the equations.

<h3>What is magnitude and sign?</h3>

5 has 5 as magnitude, and sign isn't present which means its of positive (+) sign.

-5 has 5 as magnitude and sign is negative(-).

For this case, we're multiplying both the equations but the core concept or aim is same, ie, making the coefficients of equal magnitude but with opposite sign.

<h3>Using the above facts to get the numbers to multiply the equations of the given system</h3>

The given system of equations is

\dfrac{1}{5}x + \dfrac{3}{4}y = 9\\\\\dfrac{2}{3}x - \dfrac{5}{6}y = 8

Let two numbers be p,and q who multiply equation first and second respectively to make coefficient of x of equal magnitude but opposite sign.

We have

\text{Coefficient of x in first equation}= a_1 = \dfrac{1}{5}\\\\\text{Coefficient of x in second equation} = a_2 = \dfrac{2}{3}

Multiplying with p and q will give us

p\times a_1 = \dfrac{p}{5}\\\\q \times a_2 = \dfrac{2q}{3}

We need both resultant coefficient to add up to 0, or

p/5 + 2q/3 = 0\\p = -10q/3\\q = -3p/10

Now in options, we see first equation is either getting multiplied with -10, 10, or -3,3

If we put q = 3, we get p =  -10q/3=  -10

If we put q = -3, we get p = 10

If we put q = 5, we get p = -50/3

Thus only first choice is matching the correct pairs.

Thus,

The numbers that can be multiplied by each equation so that when the two equations are added together, the x term is eliminated is given by

Option A: –10 times the first equation and 3 times the second equation

Learn more about method of elimination here:

brainly.com/question/20385690

7 0
2 years ago
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HELP PLEASE!!! :( <br> I REALLY NEED HELP ASAP!!<br><br><br> Thank you and stay safe!
Mkey [24]

Answer:

a = 6, b = -2, c = 3

Step-by-step explanation:

6x² - 2x + 3 = 0

a = 6, b = -2, c = 3

6 0
3 years ago
Read 2 more answers
Bradley is returning home from a place that is 2 kilometers away. The function y = 2,000 − 90x represents Bradley's distance fro
12345 [234]

Answer:

The function is linear

The function changes at a constant rate

Step-by-step explanation:

If this function were to be graphed, a line would be seen. It is not an increasing function because he is getting closer to home so the distance from his house is decreasing

6 0
3 years ago
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