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2 years ago

Find the inverse of each function.

Mathematics

1 answer:

weeeeeb [17]2 years ago

4 0

The inverse of a function is the opposite of the function

<h3>How to determine the inverse functions</h3>

1) y = log2 (3x)

Swap the positions of x and y

$x = \log_2(3y)$

Apply the exponential rule

$2^x = 3y$

Make y the subject

$y = \frac{2^x}3$

Hence, the inverse function is: $y = \frac{2^x}3$

2) y=log3(x-1)

Swap x and y

$x = \log_3(y - 1)$

Apply exponent rule

$3^x = y - 1$

Make y the subject

$y = 3^x + 1$

Hence, the inverse function is: $y = 3^x + 1$

3) y=-2log x

Swap x and y

$x=-2\log y$

Divide both sides by -2

$-0.5x=\log y$

Apply exponent rule

$y = 10^{-0.5x}$

Hence, the inverse function is: $y = 10^{-0.5x}$

4) y=log6(3x)

Swap x and y

$x = \log_6(3y)$

Apply exponent rule

$3y = 6^x$

Make y the subject

$y = \frac{6^x}{3}$

Hence, the inverse function is: $y = \frac{6^x}{3}$

5)y=log3(x+2)

Swap x and y

$x = \log_3(y + 2)$

Apply exponent rule

$y + 2 = 3^x$

Make y the subject

$y = 3^x - 2$

Hence, the inverse function is: $y = 3^x - 2$

6) y=log3(5^3)

Swap x and y

$x = \log_3(5^3)$

Hence, the inverse function is: $x = \log_3(5^3)$

7) y=6^x+5

Swap x and y

$x = 6^y + 5$

Subtract 5 from both sides

$6^y = x - 5$

Apply logarithm

$y = \log_6(x - 5)$

Hence, the inverse function is: $y = \log_6(x - 5)$

9) y=log3 2^x

Swap x and y

$x = \log_3(2^y)$

Apply exponent rule

$2^y = 3^x$

Apply logarithm

$y = \log_2(3^x)$

Hence, the inverse function is: $y = \log_2(3^x)$

10) y=3^x -7

Swap x and y

$x = 3^y - 7$

Add 7 to both sides

$3^y = x + 7$

Apply logarithm

$y = \log_3(x + 7)$

Hence, the inverse function is: $y = \log_3(x + 7)$

Read more about inverse functions at:

brainly.com/question/14391067

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nirvana33 [79]

6 watermelons, because each watermelon is 2 kg

4 0

2 years ago

In triangle RST, m∠R > m∠S + m∠T. Which must be true of triangle RST? Check all that apply.

solmaris [256]

Answer:

1. m∠R > 90°

2. m∠S + m∠T < 90°

4. m∠R > m∠T

5. m∠R > m∠S

Step-by-step explanation:

<h3>General strategy</h3>

prove the statement starting from known facts, or
disprove the statement by finding a counterexample

Helpful fact: Recall that the Triangle Sum Theorem states that m∠R + m∠S + m∠T = 180°.

Option 1. m∠R > 90°

Start with m∠R > m∠S + m∠T.

Adding m∠R to both sides of the inequality...

m∠R + m∠R > m∠R + m∠S + m∠T

There are two things to note here:

The left side of this inequality is 2*m∠R
The right side of the inequality is exactly equal to the Triangle Sum Theorem expression

2* m∠R > 180°

Dividing both sides of the inequality by 2...

m∠R > 90°

So, the first option must be true.

Option 2. m∠S + m∠T < 90°

Start with m∠R > m∠S + m∠T.

Adding (m∠S + m∠T) to both sides of the inequality...

m∠R + (m∠S + m∠T) > m∠S + m∠T + (m∠S + m∠T)

There are two things to note here:

The left side of this inequality is exactly equal to the Triangle Sum Theorem expression
The right side of the inequality is 2*(m∠S+m∠T)

Substituting

180° > 2* (m∠S+m∠T)

Dividing both sides of the inequality by 2...

90° > m∠S+m∠T

So, the second option must be true.

Option 3. m∠S = m∠T

Not necessarily. While m∠S could equal m∠T, it doesn't have to.

Example 1: m∠S = m∠T = 10°; By the triangle sum Theorem, m∠R = 160°, and the angles satisfy the original inequality.

Example 2: m∠S = 15°, and m∠T = 10°; By the triangle sum Theorem, m∠R = 155°, and the angles still satisfy the original inequality.

So, option 3 does NOT have to be true.

Option 4. m∠R > m∠T

Start with the fact that ∠S is an angle of a triangle, so m∠S cannot be zero or negative, and thus m∠S > 0.

Add m∠T to both sides.

(m∠S) + m∠T > (0) + m∠T

m∠S + m∠T > m∠T

Recall that m∠R > m∠S + m∠T.

By the transitive property of inequalities, m∠R > m∠T.

So, option 4 must be true.

Option 5. m∠R > m∠S

Start with the fact that ∠T is an angle of a triangle, so m∠T cannot be zero or negative, and thus m∠T > 0.

Add m∠S to both sides.

m∠S + (m∠T) > m∠S + (0)

m∠S + m∠T > m∠S

Recall that m∠R > m∠S + m∠T.

By the transitive property of inequalities, m∠R > m∠S.

So, option 5 must be true.

Option 6. m∠S > m∠T

Not necessarily. While m∠S could be greater than m∠T, it doesn't have to be. (See examples 1 and 2 from option 3.)

So, option 6 does NOT have to be true.

4 0

1 year ago

There are approximately 3.2

gladu [14]

So, using the number 3,200,000 deaths per year, you want to divide it until it reaches deaths per minute.
3,200,000 divided by 365 (for days)
8767.123 divided by 24 (for hours)
365.297 divided by 60 (for minutes)
and so you get
6.088 deaths per minute

Hope this helped.

8 0

3 years ago

What is the equation of a line with a slope of 3 and contains point (4.1)

cricket20 [7]

Answer:

y = 3x - 11

Step-by-step explanation:

y=mx+b

1=3(4)+b

1=12+b

b=-11

5 0

3 years ago

Read 2 more answers

Pls help me, I really dont understand

Stella [2.4K]

Answer:

-2.5x-.5

$y=\frac{2}{3}x-1$

draw the dotted line (3/7)x-3 and shade below it

Step-by-step explanation:

First, we need the slope

Use the slope formula:

$\frac{Y_2-Y_1}{X_2-x_1}=\frac{2-(-8)}{-1-3}=\frac{10}{-4}=-2.5$

so we have

y= -2.5x+b

Solve for b by plugging in coordiantes

-8= -2.5(3)+b

-8= -7.5+b

b= -.5

Put it together and get -2.5x-.5

2.)

A line is parallel to another line if they have the same slope (and different y intercepts)

So in the formula y=mx+b we knowe that m= 2/3

Now it's just a matter of solving for B

plug in the required coordinate to do this

-1=(2/3)*0+b

-1= b

Put it all together to get

$y=\frac{2}{3}x-1$

3.)

put this into slope intercept form

3x-7y>21

3x-21 > 7y

(3/7)x-3 >y

To graph this just draw a dotted line with the equation (3/7)x-3 and shade everything below it (use de_smos if you're stuck)

7 0

3 years ago