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krok68 [10]
3 years ago
12

If f(x) = log2 (x + 1), what is f-1(2)? (2 points)

Mathematics
2 answers:
ivolga24 [154]3 years ago
7 0

Answer:

3

Step-by-step explanation:

f^{-1}(2)=b \text{ implies } f(b)=2

This we means to to solve the following equation for b:

f(b)=\log_2(b+1)

2=\log_2(b+1) since f(b)=2

Write in equivalent exponential form:

2^2=b+1

4=b+1

Subtract 1 on both sides:

4-1=b

3=b

This means f(3)=2 \text{ so } f^{-1}(2)=3

You could actually find the inverse function if you want to then replace input for the inverse with 2.

y=\log_2(x+1)

Your logarithm has base 2 and input (x+1) and output y.

The equivalent exponential form is:

2^{y}=x+1

If we solve for x then at the end swap x and y we would have found the inverse function.

Let's do that:

2^y=x+1Subtract 1 on both sides:[tex]2^y-1=x

Swap x and y:

2^x-1=y

The inverse function of our given function is:

f^{-1}(x)=2^x-1

Now we need to replace x with 2:

f^{-1}(2)=2^2-1

f^{-1}(2)=4-1

f^{-1}(2)=3

Soloha48 [4]3 years ago
3 0

as you already know, to get the inverse of any expression, we start off by doing a quick switcheroo on the variables, and then solve for "y".

\bf \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\textit{we'll use this one}}{a^{log_a x}=x} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{f(x)}{y}=\log_2(x+1)\implies \stackrel{\textit{quick switcheroo}}{\underline{x}=\log_2(\underline{y}+1)}\implies 2^x=2^{\log_2({y}+1)} \\\\\\ 2^x=y+1\implies 2^x-1=\stackrel{f^{-1}(x)}{y} \\\\[-0.35em] ~\dotfill\\\\ 2^2-1=f^{-1}(2)\implies 3=f^{-1}(2)

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Answer:

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Step-by-step explanation:

We require to calculate the volume of 1 brick

V = lbh ( l is length, b is breadth and h is height ), that is

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5 0
3 years ago
A photo of a beetle in a science book is increased to 535​% as large as the actual size. If the beetle is 14 ​millimeters, what
AnnZ [28]

Answer: 74.9 millimeters

Step-by-step explanation:

From the question, a photo of a beetle in a science book was.increased to 535​% as large as its actual size and the beetle.has a actual size of 14 ​millimeters,

The size of the beetle on the photo will be 535% of 14 millimeters. This will be:

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4 0
3 years ago
What is 70 times five
Burka [1]

Answer:

350

Step-by-step explanation:

7 0
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Read 2 more answers
In 1990, 1000 adults were randomly selected and each was asked if they smoked, 300
Oduvanchick [21]

Answer:

 The proportion of smokers was higher in 1990 than in 2000

Step-by-step explanation:

Solution

Recall that,

The total number of sample 1 (n1) = 1000

Total  sample 2 number  (n2) = 2000

The number of favourable events (X1) = 300

The number of favourable events (X2) = 500

so,

p₁ = X₁/n₁ = 300/1000 = 0.3

p₂ = X₂/n₂ =500/2000 =0.25

α = 0.05

We are interested in testing the hypothesis.

The  hypothesis (Null) ....>  H₀ : p₁ = p₂

Alternate hypothesis------ > H₁ : p₁ > p₂

Thus,

P = X₁ + X₂/ n₁ + n₂

P =300 + 500/1000 +2000

P =800/3000

=0.2667

Now,

Z₀ = P₁ - P₂/√ P (1 -P) (1/n₁ + 1/n₂)

Z₀ =  0.3 - 0.25/√0.2667  (1 - 0.2667) (1/1000 + 1/2000)

Z₀ = 0.4999999999999999/√ 0.2667 (0.7333000000000001) (0.001 +0.0005)

Then,

Z₀ = 0.4999999999999999/√0.00029335666500000004

Z₀ = 2.9193

so,

zα/2 = z0.05/2 =z0.025

zα/2 = 1.6448536269514722

Now, we apply the decision rule:

Decision Rule: Reject the null hypothesis if the statistic value test is higher than the critical value 1.6448536269514722

The statistic value, 2.9193 is greater than the critical value 1.6448536269514722,  then we will reject the null hypothesis.

Therefore, the proportion of smokers was higher in 1990 than in 2000

3 0
3 years ago
Convert the angle 117 radians to degrees.
Simora [160]

Answer:

21060°

Step-by-step explanation:

117x180°

=21060°

4 0
3 years ago
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