1

What is the inverse of the function f(x) = 2x + 1?

Luda [366]

Answer:

$f^{-1}(x)=\frac{1}{2}x-\frac{1}{2}$ ⇒ answer 1

Step-by-step explanation:

* Lets explain how to find the inverse of a function

- To find the inverse of a function :

# Write y = f(x)

# Switch the x and y

# Solve to find the new y

# The new y is $f^{-1}$

* Lets solve the problem

∵ f(x) = 2x + 1

- Put y = f(x)

∴ y = 2x + 1

- Switch x and y

∴ x = 2y + 1

- Solve to find the new y

∵ x = 2y + 1

- Subtract 1 from both sides

∴ x - 1 = 2y

- Divide both sides by 2

∴ (x - 1)/2 = y

- Divide each term in the left hand side by 2

∴ y = 1/2 x - 1/2

- Replace y by $f^{-1}$

∴ $f^{-1}(x)=\frac{1}{2}x-\frac{1}{2}$

* The inverse of the function is $f^{-1}(x)=\frac{1}{2}x-\frac{1}{2}$

7 0

3 years ago

Read 2 more answers

National data indicates that 35% of households own a desktop computer. In a random sample of 570 households, 40% owned a deskt

Elan Coil [88]

Answer:

Yes, this provide enough evidence to show a difference in the proportion of households that own a desktop.

Step-by-step explanation:

We are given that National data indicates that 35% of households own a desktop computer.

In a random sample of 570 households, 40% owned a desktop computer.

Let p = population proportion of households who own a desktop computer

SO, Null Hypothesis, $H_0$ : p = 25% {means that 35% of households own a desktop computer}

Alternate Hypothesis, $H_A$ : p $\neq$ 25% {means that % of households who own a desktop computer is different from 35%}

The test statistics that will be used here is One-sample z proportion statistics;

T.S. = $\frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of 570 households who owned a desktop computer = 40%

n = sample of households = 570

So, test statistics = $\frac{0.40-0.35}{{\sqrt{\frac{0.40(1-0.40)}{570} } } } }$

= 2.437

Since, in the question we are not given with the level of significance at which to test out hypothesis so we assume it to be 5%. Now at 5% significance level, the z table gives critical values of -1.96 and 1.96 for two-tailed test. Since our test statistics doesn't lies within the range of critical values of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that % of households who own a desktop computer is different from 35%.

3 0

3 years ago

Which experiment describes a binomial experiment?

marshall27 [118]

Answer: the last option.
A binomial experiment is an experiment with only two possible outcomes.

In the first option, there is three possible outcomes (i.e. A, B, C)
In the second option, there is four poissible outcomes (i.e. ace, king, queen, jack)
The third option has six possible outcomes (i.e. six faces of a die)
In the last option, there are two possible outcomes (i.e. '2 number cubes')

6 0

3 years ago

Tanya and three friends have saved $75 to help protect the pandas. If they each gave the same amount, how much did each person c

Ber [7]

Answer:

Step-by-step explanation:

If it is Tanya and 3 friends, there are 4 people in total. If they all contributed the saem amount, you would do 75/4= 18.75 dollars each

8 0

3 years ago

3. You can ride your bike 1/5 of a mile per minute. If it takes you 3 1/3 minutes to get

Allushta [10]

Answer:

2/3

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

6 0

3 years ago