All categories

2 years ago

The function of f (x) is defined by f (x)=4x+7. the inverse of f (x) is g (x). what is g (15)?

Mathematics

1 answer:

scoray [572]2 years ago

3 0

Answer:

g(15) = 2

General Formulas and Concepts:

Pre-Alg

Order of Operations: BPEMDAS
Equality Properties

Algebra I

Function inverses

Step-by-step explanation:

Step 1: Define

f(x) = 4x + 7

g(x) = f⁻¹(x)

g(15) is x = 15

Step 2: Find inverse

Rewrite: y = 4x + 7
Swap: x = 4y + 7
Isolate y term: x - 7 = 4y
Isolate y: (x - 7)/4 = y
Rewrite: y = (x - 7)/4
Back-substitute: g(x) = (x - 7)/4

Step 3: Evaluate

Substitute: g(15) = (15 - 7)/4
Subtract: g(15) = 8/4
Divide: g(15) = 2

You might be interested in

If ax + y=23, 3x - y = 9, and x =8, what is the value of a ?

inna [77]

Answer:

a = 1

Step-by-step explanation:

x = 8

3x - y = 9

3(8) - y = 9

24 - y = 9

-y = 9 - 24

-y = -15

y = 15

ax + y = 23

a(8) + 15 = 23

8a = 23 - 15

8a = 8

a = 8/8

a = 1

6 0

2 years ago

Can someone pls help me solved this problem! I need help help can someone help me I will mark you as brainiest! But plz help me!

Vilka [71]

Answer:

The number is less than 3.5

Step-by-step explanation:

Let us break up and convert each individual phrase into its equivalent in an equation.

"Three time" is $3*$

"The difference of a number and three" is (3-x)

"Is greater than" is >

"The number decreased by five" is (x-5)

We can now put all of these parts together to get our equation

$3*(3-x)>(x-5)$

Now, we can simplify this and solve for x

$3*(3-x)>(x-5)\\\\9-3x>x-5\\\\14>4x\\\\\frac{14}{4} >x\\\\\\frac{7}{2}>x\\\\x$

5 0

2 years ago

Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 7.1 parts

satela [25.4K]

Answer:

$t=\frac{6.6-7.1}{\frac{1.0}{\sqrt{26}}}=-2.550$

Step-by-step explanation:

Data given and notation

$\bar X=6.6$ represent the sample mean

$s=1.0$ represent the sample standard deviation

$n=26$ sample size

$\mu_o =7.1$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is different from 7.1 ppm, the system of hypothesis would be:

Null hypothesis: $\mu = 7.1$

Alternative hypothesis: $\mu \neq 7.1$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{6.6-7.1}{\frac{1.0}{\sqrt{26}}}=-2.550$

5 0

2 years ago

A bookseller bought 80 books at rs 30 each 20 books were stolen and he sold the remaining books at 5% loss find the selling pric

Blizzard [7]

Answer:

rs 38.

Step-by-step explanation:

Total cost of the 80 books = 80*30 = rs 2400.

He had 60 books to sell and made a 5% loss.

Thus his income from these books was 2400 - 0.05*2400 = rs 2280.

So the selling price of each book was 2280 / 60 = rs 38.

8 0

2 years ago

PLZ HELP vgffdhstudfhgxd

olga55 [171]

Answer:

1/5

Step-by-step explanation:

To simplify, we can first divide the top and bottom by 10:

2/10

Then by 2:

1/5

6 0

2 years ago

Read 2 more answers