MATHEMATICS COLLEGE

Find the domain of f and f −1 and its domain. f(x) = ln(ex − 3). (a) Find the domain of f. (Enter your answer using interval notation.) (−2,[infinity]) (b) Find f −1. f −1(x) = x+ln(3)

Answers

Answer 1

Answer:

Answer:

a.Domain of f=(1.099, $\infty)$

b. $f^(-1)(x)=ln(e^x+3)$

Step-by-step explanation:

Let $y=f(x)=ln(e^x-3)$

We know that domain of ln x is greater than zero

$e^x-3>0$

Adding 3 on both sides of inequality

$e^x-3+3>0+3$

$e^x>3$

Taking on both sides of inequality

$lne^x>ln 3$

$x>ln 3$ =1.099

By using $lne^x=x$

Domain of f=(1.099, $\infty)$

Let $y=f^(-1)(x)=ln(e^x-3)$

$e^y=e^x-3$

By using property $lnx=y\implies x=e^y$

$e^x=e^y+3$

Taking ln on both sides of equality '

$lne^x=ln(e^y+3)$

$x=ln(e^y+3)$

Replace x by y and y by x

$y=ln(e^x+3)$

Substitute y= $f^(-1)(x)$

$f^(-1)(x)=ln(e^x+3)$

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If you’re good at Geometry, can you help me with some math equations?

Answers

Answer:

sure!

Step-by-step explanation:

Answer:

What questions excatly. I'm in geometry class but I can only answer some questions

Step-by-step explanation:

Give an example of a like term for each of the following: a. 14y b. -9b c. 200 d. h^2

Answers

Answer:

a. 14y + 7y+ 8y

b. -9b + 9b+ 2b

c. 200 - 100 - 100

d. h^2 + h^2 + h^2

Step-by-step explanation:

They are like terms since you can add them.

Please give brainliest (:

Good Luck

Consider the following system of equations:Equation 1: 82 + 2y = 30
Equation 2: 70 + 2y = 24
Which variable pair should we try to eliminate?
The x's because the coefficients are the same.
The y's because the coefficients are the same.
The x's because the coefficients are different?
The y's because the coefficients are different?

Answers

The correct answer is: "The y's because the coefficients are the same."

Further explanation:

we always try to eliminate the variable from the system of equations which involves lesser calculations and complexity.

Assuming that Given equations are:

Equation 1: 82x + 2y = 30

Equation 2: 70x + 2y = 24

we can see that the coefficients of x are very large and different. While the coefficients of y are same. We can only subtract the equations to eliminate y.

Hence,

The correct answer is: "The y's because the coefficients are the same."

Keywords: Linear equations, variables

Learn more about linear equations at:

#LearnwithBrainly

...........................

Answers

Answer: growth, rate is 95.8%
The base 1.958 is in the form 1+r where
1+r = 1.958
r = 1.958-1
r = 0.958
r = 95.8%
The value of r is positive indicating we have growth.
Contrast this to something like 1+r = 0.8 and that solves to r = -0.20 = -20% to indicate decay of 20%. In other words, if the base were some positive number less than 1, then you have decay. Otherwise, you have growth.
The initial value 880 does not affect the answer, so we completely ignore it.

Why is 8 thousandths + 6 ones 8 thousandths = 76?

Answers

Answer:

8 thousandths + 6 ones 8 thousandths = 6016 thousandths

Step-by-step explanation:

Answer:

I think it is 16006

Step-by-step explanation:

this because 8 thousands=8000

8000+6=8006

soooo,

8000+8006=16006 is the answer

hope you find it useful

A calzone is divided into 24 equal pieces. Sophie and Glenn each ate one-fourthof the calzone on Saturday. The next day, Glenn ate one-sixth
of the calzone that was leftover. How many of the pieces of the original calzone remain? Explain your reasoning.