If f(x) = x^3, find x if f(x) = 1000

help!!

A composite function is the combination of multiple functions.

The correct answers are:

1. Test for inverse function

To test if two functions are inverse of one another, we simply find their composites.

Assume the functions are g(x) and h(x).

We simply test for and

If they are equal, then both functions are inverse functions

2. Inverse of f(x) = 3x

Rewrite as:

Swap y and x

Make y the subject

Hence, the inverse function is:

3. True statements

A function has unique ordered pairs; so, it will pass the vertical line test.

Because it has unique ordered pairs, the inverse function will pass the vertical line tests, and the horizontal line tests.

Hence;

(b) All answers are correct

4. Inverse of

Rewrite as:

Swap x and y

Solve for y: Divide both sides by 3

Take cube roots of both sides

Add 2 to both sides

Hence, the inverse function is:

5. The inverse of

Rewrite as:

Swap x and y

Solve for y: Add 3 to both sides

Divide both sides by 2

Hence, the inverse function is:

Read more about inverse functions at:

link

A composite function is the combination of multiple functions.

The correct answers are:

1. Test for inverse function

To test if two functions are inverse of one another, we simply find their composites.

Assume the functions are g(x) and h(x).

We simply test for and

If they are equal, then both functions are inverse functions

2. Inverse of f(x) = 3x

Rewrite as:

Swap y and x

Make y the subject

Hence, the inverse function is:

3. True statements

A function has unique ordered pairs; so, it will pass the vertical line test.

Because it has unique ordered pairs, the inverse function will pass the vertical line tests, and the horizontal line tests.

Hence;

(b) All answers are correct

4. Inverse of

Rewrite as:

Swap x and y

Solve for y: Divide both sides by 3

Take cube roots of both sides

Add 2 to both sides

Hence, the inverse function is:

5. The inverse of

Rewrite as:

Swap x and y

Solve for y: Add 3 to both sides

Divide both sides by 2

Hence, the inverse function is:

Read more about inverse functions at:

link

Step-by-step explanation:

Exponential growth is the change that occurs when an original amount is increased by a constant rate over a period of time.

The exponential function is given by y=

, where A is the initial amount , b is the rate of growth and x is the time period.

Therefore, is only function in the given options which is exponential.

x = 10

Step-by-step explanation:

x = -1, 3, and 7

Step-by-step explanation:

Using grouping:

f(x) = x³ − 9x² + 11x + 21

f(x) = x³ − 9x² + 18x − 7x + 21

f(x) = x (x² − 9x + 18) − 7 (x − 3)

f(x) = x (x − 6) (x − 3) − 7 (x − 3)

f(x) = (x² − 6x) (x − 3) − 7 (x − 3)

f(x) = (x² − 6x − 7) (x − 3)

f(x) = (x + 1) (x − 7) (x − 3)

To use long division, see the picture.

The zeros are x = -1, 3, and 7.

x = -1, 3, and 7

Step-by-step explanation:

Using grouping:

f(x) = x³ − 9x² + 11x + 21

f(x) = x³ − 9x² + 18x − 7x + 21

f(x) = x (x² − 9x + 18) − 7 (x − 3)

f(x) = x (x − 6) (x − 3) − 7 (x − 3)

f(x) = (x² − 6x) (x − 3) − 7 (x − 3)

f(x) = (x² − 6x − 7) (x − 3)

f(x) = (x + 1) (x − 7) (x − 3)

To use long division, see the picture.

The zeros are x = -1, 3, and 7.

9514 1404 393

  x = {7, 1, -4}

Step-by-step explanation:

Dividing the given factor from the polynomial using synthetic division, we get ...

  f(x) = (x -7)(x^2 +3x -4)

Factoring the quadratic* gives ...

  f(x) = (x -7)(x -1)(x +4)

The zeros are the values of x that make these factors be zero:

  x = {7, 1, -4}

_____

* The constants in the binomial factors are factors of -4 that have a sum of +3. Those are (-1)(4) = -4. -1+4 = 3.

9514 1404 393

  x = {7, 1, -4}

Step-by-step explanation:

Dividing the given factor from the polynomial using synthetic division, we get ...

  f(x) = (x -7)(x^2 +3x -4)

Factoring the quadratic* gives ...

  f(x) = (x -7)(x -1)(x +4)

The zeros are the values of x that make these factors be zero:

  x = {7, 1, -4}

_____

* The constants in the binomial factors are factors of -4 that have a sum of +3. Those are (-1)(4) = -4. -1+4 = 3.

f(x) = x2 – 10x + 21

Step-by-step explanation:

I got it because you substract and add the last part