All categories

2 years ago

Given the function f(x) = 3x, find the value of f−1(81).

1 answer:

4 0

Given the function f (x) = 3x, find the value of f-1 (81).
For this case, the first thing you should do is rewrite the function.
We have then:
y = 3 ^ x
From here, we clear the value of x:
log3 (y) = log3 (3 ^ x)
log3 (y) = x
Then, we rewrite the function again:
f (x) ^ - 1 = log3 (x)
Now, we evaluate the inverse function for x = 81:
f (81) ^ - 1 = log3 (81)
f (x) ^ - 1 = 4
Answer:
the value of f-1 (81) is:
f (x) ^ - 1 = 4

You might be interested in

What is the domain of the given function? <br> {(3,-2), (6, 1), (-1,4), (5,9), (-4,0)}

grandymaker [24]

Answer:

D = { -4,-1,3,5,6}

Step-by-step explanation:

The domain is the x values or the inputs

D = { 3,6,-1,5,-4}

We normally put them in order from smallest to largest

D = { -4,-1,3,5,6}

4 0

2 years ago

A graph in which the frequency for each category of a quantitative variable is represented as a vertical column that touches the

Arturiano [62]

Answer:

Histogram.

Step-by-step explanation:

Such a Graph is called Histogram.

A histogram can be defined as a visual representation of data in form of bars of different heights. In histogram, each and every bar groups numbers into ranges. The greater the height of the bar, the larger the data falls into its range. It basically represents shape and spread of continuous data sample.

3 0

1 year ago

Patrick decided to run every day to keep himself healthy. He ended up running

Over [174]

Answer:

Well, you gotta take the amount a person runs per day and multiply by seven to see how much they ran per week, i dont have a value so its not possible to answer the quistion.

5 0

2 years ago

Marcie bought a total of 20 used books and cds during a yard sale for a total of 54.50$. of books cost 1.50$ each and cds 5$ eac

melomori [17]

Let numbers of books be 'b' and numbers of CDs be 'c'

We can set up two equations:
Equation [1] ⇒ $b+c=20$
Equation [2] ⇒ $1.50b+5c=54.50$

We are solving for the number of books and the number of CDs bought

When we have two equations in terms of two different variables; $b$ and $c$ , that we need to solve, then this becomes a simultaneous equation problem.

First, rearrange Equation [1] to make either $b$ or $c$ the subject:
$b+c=20$
$b=20-c$

Then we substitute $b=20-c$ into Equation [2]
$1.50b+5c=54.50$
$1.50(20-c)+5c=54.50$
$30-1.50c+5c=54.50$
$5c-1.5c=54.50-30$
$3.5c=24.50$
$c=7$

Now we know the value of $c$ which is $c=7$ , substitute this value into $b=20-c$ we have $b=20-7=13$

Answer:
Numbers of books = 13
Numbers of CDs = 7

5 0

2 years ago

What is the following product? (StartRoot 12 EndRoot + StartRoot 6 EndRoot) (StartRoot 6 EndRoot minus StartRoot 10 EndRoot)

Crank

Answer:

The product results in: $6\,\sqrt{2} -2\,\sqrt{30} +6-2\,\sqrt{15}$ , which agrees with answer A of the given choices.

Step-by-step explanation:

We need to apply distributive property for the product of two expressions each consisting of two terms, and also use the properties of products of radicals of the same root:

$(\sqrt{12} +\sqrt{6} )(\sqrt{6} -\sqrt{10} )=\\=\sqrt{12*6} -\sqrt{12*10} +\sqrt{6*6} -\sqrt{6*10} =\\=\sqrt{72} -\sqrt{120} +\sqrt{36} -\sqrt{60}$

and now, we extract as many factors we can from the roots to reduce them:

$\sqrt{72} -\sqrt{120} +\sqrt{36} -\sqrt{60} =\\=6\,\sqrt{2} -2\,\sqrt{30} +6-2\,\sqrt{15}$

5 0

2 years ago

Read 2 more answers