All categories

3 years ago

An exponential function is the inverse of a logarithmic function. A)True B)False

Mathematics

2 answers:

Igoryamba3 years ago

7 0

the correct answer is

A) True

jonny [76]3 years ago

3 0

Answer:

The given statement is true.

Step-by-step explanation:

The graph of the inverse function is reflection about the line y = x from the graph of the function.

Apart from these the domain of the inverse function is the range of the function and the range of the inverse function is the domain of the function.

Let us graph the functions $y=e^x$ and $y=\ln x$

The exponential function always passes through the point (0,1) and logarithm function passes through the point (1,0).

From the graph we can see that the graph of exponential function is the reflection about the line y=x.

Hence, exponential function is the inverse of a logarithmic function.

Thus, the given statement is true.

You might be interested in

A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 35 adult Americans an

Y_Kistochka [10]

Answer: a) 15, b) 1.

Step-by-step explanation:

A researcher studying public opinion of proposed social security changes obtains a simple random sample of 35 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more Americans does the researcher need to sample in the following cases?

(a) 10% of all adult Americans support the changes

Here, $np>5\ and\ n(1-p)>5$

And , $p=0.10$

So, consider the equality, to find the value of 'n'.

$np=5\\\\n\times 0.10=5\\\\n=\dfrac{5}{0.10}\\\\n=50$

So, there are $50-35=15$ more adult Americans needed.

(b) 15% of all adult Americans supports the changes

Here, $p=0.15$

So, again we get that

$np=5\\\\n\times 0.15=5\\\\n=\dfrac{5}{0.15}\\\\n=33.33\\\\n\approx 34$

So, there are $35-34=1$ more adult Americans needed.

Hence, a) 15, b) 1.

5 0

4 years ago

Write each ratio in the simplest form 35 to 105

Sedaia [141]

Answer: 35:105=1:3

Hope this helps! Have a good day !!! :)

8 0

2 years ago

Rebecca sells greetings cards at £1.47 each. She donates 3 7 of this money to a charity. How much does the charity receive from

ANTONII [103]

The charity receive £54.39 form the sale of each card.

4 0

3 years ago

Taylor and Anya are friends who live 63 miles apart. Sometimes on a Saturday, they ride toward each other's houses on their bike

marishachu [46]

Solutions

Solution: Finding distances first

Since the bike ride took 3 hours, Taylor must have ridden 37.5 miles. Therefore Anya must have ridden 63 - 37.5 - 25.5 miles. If we divide the distance Anya rode by the amount of time it took her to ride, we will get her speed (assuming she rode at a constant speed).

25.5 miles ÷3 hours =8.5 miles per hour.

So if Anya rode at a constant speed, she was traveling 8.5 miles per hour.

Solution: Subtracting Taylor's speed from total speed

The distance between the two friends is decreasing by

63 miles ÷3 hours =21 miles per hour.

Since Taylor rides at 12.5 miles per hour, Anya's speed must be 21 - 12.5 = 8.5 miles per hour. Solutions

Solution: Finding distances first

25.5 miles ÷3 hours =8.5 miles per hour.

So if Anya rode at a constant speed, she was traveling 8.5 miles per hour.

Solution: Subtracting Taylor's speed from total speed

The distance between the two friends is decreasing by

63 miles ÷3 hours =21 miles per hour.

Since Taylor rides at 12.5 miles per hour, Anya's speed must be 21 - 12.5 = 8.5 miles per hour.

Assuming Anya rode at a constant speed, she was traveling 8.5 miles per hour.

5 0

3 years ago

I am Lyosha [343]

You have the right idea that things need to get multiplied.

What should be done is that the entire fraction needs to get multipled by the lowest common denominator of both denominators.

Let's look at the complex numerator. Its denominators are 5 and x + 6. Nothing is common with these, so both pieces are needed.

The complex denominator has x - 3 as its denominator. With nothing in common between it and the complex numerator, that piece is needed.

So we multiply the entire complex fraction by (5)(x + 6)(x -3).

Numerator: $(\frac{1}{5} -\frac{5}{x + 6})(5)(x +6)(x-3) =\frac{1}{5}(5)(x +6)(x-3) - \frac{5}{x + 6}(5)(x +6)(x-3)$

= (x+6)(x-3) - (5)(5)(x-3)

= (x+6)(x-3) - 25(x-3)

= (x-3)(x + 6 - 25) <--- by group factoring the common x - 3

= (x -3)(x - 19)

Denominator:

$\frac{25}{x - 3} * (5)(x + 6)(x - 3) = (25)(5)(x + 6) = 125(x + 6)$

Now we put the pieces together.

Our fraction simplies to (x - 3) (x - 19) / 125 (x + 6)

5 0

4 years ago