1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
larisa [96]
2 years ago
11

Which of these functions has an inverse function? Select all that apply.

Mathematics
2 answers:
allochka39001 [22]2 years ago
6 0

Answer:

The function x=y and y=x^{3} are inverse function.

Step-by-step explanation:

Function inverse definition:

If a provided function <em>f(x)</em> is mapped <em>x</em> to <em>y</em>, then the inverse of the provided function <em>f(x) </em>is mapped <em>y</em> to <em>x</em>.

Or  f(x)=f(y)\Rightarrow x=y

Now, consider the function <em>y</em> =<em> x</em>.

Interchange the variables <em>x</em> and <em>y</em>.

x=y

Now, solve x=y for y.

x=y

Therefore, this function has an inverse.

Consider the function y=x^{2}.

Interchange the variables <em>x</em> and <em>y</em>.

x=y^{2}

Now, solve x=y^{2} for y.

\pm \sqrt{x} =y

Therefore, the function has no inverse.

Consider the function y=x^{3}.

Interchange the variables <em>x</em> and <em>y</em>.

x=y^{3}

Now, solve x=y^{3} for y.

\sqrt[3]{x}=y

Therefore, the function has inverse.

Consider the function y=x^{4}.

Interchange the variables <em>x</em> and <em>y</em>.

x=y^{4}

Now, solve x=y^{4} for y.

\pm \sqrt[4]{x}=y

Therefore, the function has no inverse.

Hence, the function x=y and y=x^{3} are inverse function.

ElenaW [278]2 years ago
5 0

ANSWER

y=x

y=x³

EXPLANATION

A function, f(x) has an inverse if and only if

f(a) = f(b)   \Rightarrow \: a = b

Thus, the function is one to one.

For y=x or

f(x) = x

f(a) = f(b)   \Rightarrow \: a = b

Hence this function has an inverse.

For the function y=x² or f(x)=x².

f(a) = f(b)   \Rightarrow \:  {a}^{2} =  {b}^{2} \Rightarrow \: a =  \pm \: b

This function has no inverse on the entire real numbers.

For the function y=x³ or f(x)=x³

f(a) = f(b)   \Rightarrow \:  {a}^{3} =  {b}^{3} \Rightarrow \: a = b

This function also has an inverse.

For y=x⁴ or f(x) =x⁴

f(a) = f(b)   \Rightarrow \:  {a}^{4} =  {b}^{4} \Rightarrow \: a =  \pm \: b

This function has no inverse over the entire real numbers.

You might be interested in
Which point-slope equation represents a line that passes through (3,-2) with a slope of -4/5?
Viefleur [7K]

Answer:

y + 2 = -4/5 (x - 3)

Step-by-step explanation:

y - y1 = m (x - x1). Put in your points for y1 and x1, and always remember to flip your signs.

unfortunately, I don't know why that isn't one of your answers, so sticking with the positive 2 I would choose y+2=- (- 3) if I were you. Looks like the -4/5 disappeared somehow?

Hope this helps

8 0
2 years ago
The regular price of a video game is $19.50 The store is having a 40% off sale.
Afina-wow [57]
A. The discount is 7.80 much

B. $11.7
7 0
3 years ago
A geometry student wants to draw a rectangle inscribed in the ellipse
IceJOKER [234]
What is the question?
6 0
3 years ago
One sample has a mean of and a second sample has a mean of . The two samples are combined into a single set of scores. What is t
Murrr4er [49]

Answer:

a) For this case we can use the definition of weighted average given by:

M = \frac{ \bar X_1 n_1 + \bar X_2 n_2}{n_1 +n_2}

And if we replace the values given we have:

M = \frac{8*4 + 16*4}{4+4}= 12

b) M = \frac{8*3 + 16*5}{3+5}= 13

c) M = \frac{8*5 + 16*3}{5+3}= 11

Step-by-step explanation:

Assuming the following question: "One sample has a mean of M=8 and a second sample has a mean of M=16 . The two samples are combined into a single set of scores.

a) What is the mean for the combined set if both of the original samples have n=4 scores "

For this case we can use the definition of weighted average given by:

M = \frac{ \bar X_1 n_1 + \bar X_2 n_2}{n_1 +n_2}

And if we replace the values given we have:

M = \frac{8*4 + 16*4}{4+4}= 12

b) what is the mean for the combined set if the first sample has n=3 and the second sample has n=5

Using the definition we have:

M = \frac{8*3 + 16*5}{3+5}= 13

c) what is the mean for the combined set if the first sample has n=5 and the second sample has n=3

Using the definition we have:

M = \frac{8*5 + 16*3}{5+3}= 11

7 0
3 years ago
Alyssa invests $2600 in a savings account at 9% simple interest. How much does she have in her account after 3 years?
pogonyaev

Answer:

$3,302

Step-by-step explanation:

9% x 3 (years) = 27%

$2600 x 27% = 702

$2600 + 702 = $3302

4 0
3 years ago
Read 2 more answers
Other questions:
  • Find the missing coefficient (5d - 7)(5d - 6) = 25d2 + what d + 42
    8·1 answer
  • Drag steps in the given order to evaluate this<br> expression.<br> (-5)(2) – 2(-3) + 3
    6·1 answer
  • Find a.b. IaI =3, IbI = 5 the angle between a and b is 2π/3
    15·1 answer
  • Achilles ordered a pizza with 16 slices. Every hour, he ate half of the remaining slices. Let f(n) be the number of slices Achil
    14·1 answer
  • 4(2x-3)+8(x-4)=2(2x+6) help plzzz
    9·2 answers
  • Can U guys please help with this. :)
    12·1 answer
  • Find the indicated limit, if it exists. limit of f of x as x approaches negative 1 where f of x equals 4 minus x when x is less
    14·1 answer
  • Paulo and Marie are collecting quarters. The number of quarters Paulo has is 3 times 5 fewer than the number of quarters Marie h
    11·1 answer
  • Under his cell phone plan, Parker pays a flat cost of $36.50 per month and $5 per gigabyte. He wants to keep his bill under $45
    11·1 answer
  • BRAINLIEST TO THE CORRECT ANSWER! 20 POINTS!!
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!