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3 years ago

If f(x)=3x+2 what is the equation for f^-1(x)

Mathematics

1 answer:

Elden [556K]3 years ago

4 0

Answer:

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

Step-by-step explanation:

To find the inverse function, swap x and y, then solve for y.

y = 3x +2 . . . . given function

x = 3y +2 . . . . inverse relation

x -2 = 3y . . . . subtract 2

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

f^-1(x) = (x -2)/3 . . . . in functional form

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Use the product of powers property to simplify the numeric expression.

motikmotik

Answer:

The value of $4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}$ is $4^{\dfrac{8}{15}}$ .

Step-by-step explanation:

We need to simplify the numeric expression using property. The expression is as follows :

$4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}$

The property to be used is : $x^a{\cdot} x^b=x^{a+b}$

This property is valid if the base is same. Here, base is x.

In this given problem, x = 4, a = 1/3 and b = 1/5

So,

$4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}}=4^{\dfrac{1}{3}+\dfrac{1}{5}}\\\\=4^{\dfrac{5+3}{15}}\\\\=4^{\dfrac{8}{15}}$

So, the value of $4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}$ is $4^{\dfrac{8}{15}}$ .

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3 years ago

Solve the following quadratic equation:<br><br> y=5x2+10x<br> Solutions: x= and x=

Brilliant_brown [7]

Answer:

0 and -2

Step-by-step explanation:

$5x^2+10x=0\\5x(x+2)=0\\\\Then\\5x=0\\\\x=\frac{0}{5}==>x_{1}=0 \\x+2=0==> x_{2}=-2$

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2 years ago

The mathematics club is selling pizza for $2 per slice and lemonade for $1 per bottle to raise money for a trip. They estimate t

german

Answer:

your answer is 453

Step-by-step explanation:

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2 years ago

Pennsylvania has a land mass of 44,816 square miles.What is the land area of Pennsylvania rounded to the nearest hundred?

sineoko [7]

The answer would be 44,800 if you want to round the hundreds place

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2 years ago

Item 19 The scale on a map is 1 cm:30 mi. The distance on the map between San Francisco, CA, and Chicago, IL, is 61.9 cm. What i

Harlamova29_29 [7]

Answer:

1857 miles.

Step-by-step explanation:

We have been given that the scale on a map is 1 cm:30 mi. The distance on the map between San Francisco, CA, and Chicago, IL, is 61.9 cm. We are asked to find the actual distance between San Francisco and Chicago.

We will use proportions to solve our given problem.

$\frac{\text{Actual distance}}{\text{Map distance}}=\frac{30\text{ miles}}{1\text{ cm}}$

Upon substituting map distance between San Francisco and Chicago, we will get:

$\frac{\text{Actual distance}}{61.9\text{ cm}}=\frac{30\text{ miles}}{1\text{ cm}}$

$\frac{\text{Actual distance}}{61.9\text{ cm}}\cdot 61.9\text{ cm}=\frac{30\text{ miles}}{1\text{ cm}}\cdot 61.9\text{ cm}$

$\text{Actual distance}=30\text{ miles}\cdot 61.9$

$\text{Actual distance}=1857\text{ miles}$

Therefore, the actual distance between San Francisco and Chicago is 1857 miles.

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3 years ago