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3 years ago

Given the function f(x) = 2^x, find the value of f^−1(32).

Mathematics

1 answer:

klio [65]3 years ago

5 0

$f(x)= 2^{x}$

We are to find the value of $f^{-1}(32)$

First we need to find the inverse of f(x) . The inverse of $2^{x}$ is $\frac{ln(x)}{ln(2)}$ .

Steps to find inverse of f(x) are shown below in the image.

So $f^{-1}(32)$ = $\frac{ln(32)}{ln(2)}=5$

Therefore, the correct answer is option C

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Х = 2y — 4<br> (3х – бу = -12

horsena [70]

Answer:

Step-by-step explanation:

Substitute the value of x to the 2nd equation

3(2y-4)-6y=-12

6y-12-6y=-12

0=0

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3 years ago

What will be the value of

madreJ [45]

The expression as given doesn't make much sense. I think you're trying to describe an infinitely nested radical. We can express this recursively by

$\begin{cases}a_1=\sqrt{42}\\a_n=\sqrt{42+a_{n-1}}\end{cases}$

Then you want to know the value of

$\displaystyle\lim_{n\to\infty}a_n$

if it exists.

To show the limit exists and that $a_n$ converges to some limit, we can try showing that the sequence is bounded and monotonic.

Boundedness: It's true that $a_1=\sqrt{42}\le\sqrt{49}=7$ . Suppose $a_k\le 7$ . Then $a_{k+1}=\sqrt{42+a_k}\le\sqrt{42+7}=7$ . So by induction, $a_n$ is bounded above by 7 for all $n$ .

Monontonicity: We have $a_1=\sqrt{42}$ and $a_2=\sqrt{42+\sqrt{42}}$ . It should be quite clear that $a_2>a_1$ . Suppose $a_k>a_{k-1}$ . Then $a_{k+1}=\sqrt{42+a_k}>\sqrt{42+a_{k-1}}=a_k$ . So by induction, $a_n$ is monotonically increasing.

Then because $a_n$ is bounded above and strictly increasing, the limit exists. Call it $L$ . Now,

$\displaystyle\lim_{n\to\infty}a_n=\lim_{n\to\infty}a_{n-1}=L$

$\displaystyle\lim_{n\to\infty}a_n=\lim_{n\to\infty}\sqrt{42+a_{n-1}}=\sqrt{42+\lim_{n\to\infty}a_{n-1}}$

$\implies L=\sqrt{42+L}$

Solve for $L$ :

$L^2=42+L\implies L^2-L-42=(L-7)(L+6)=0\implies L=7$

We omit $L=-6$ because our analysis above showed that $L$ must be positive.

So the value of the infinitely nested radical is 7.

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3 years ago

The approximate value of 4 times 10 Superscript 9 divided by left parenthesis 1.5 times 10 Superscript 6 right parenthesis is

sashaice [31]

Simplify the expression. Write the answer in scientific notation. left parenthesis 9 times 10 Superscript negative 4 right parenthesis left parenthesis 6 times 10 Superscript negative 5 right parenthesis(9×10−4)(6×10−5)

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4 years ago

Can someone help me with this question with details

Rufina [12.5K]

Answer:

I think the answer is 5 ( if wrong then do a low rating)

Step-by-step explanation:

The way I found the answer was by using PEDMAS so first I handled [(4 - (-5)) x (-7)] which is the same as 4 + -5 which equals -1 and when multiplied by -7 equals positive 7 because whenever you multiply 2 negatives you get a positive.

Next I solved 6 / (-3) which is -2 since whenever a positive is divided by a negative the quotient is negative. Now the equation is:

-2 + 7 and when solved is -2 + 7 = 5

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2 years ago

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