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3 years ago

Let f(x) = (6x^3 – 7)^3 and g(x) = 6x^3 - 7. Given that f(x) = (hog)(x), find h(x).

Mathematics

2 answers:

Katena32 [7]3 years ago

7 0

Answer:

h(x) = x^3.

Step-by-step explanation:

h(x) = x^3

because (h o g)(x) = (6x^3 - 7)^3.

alexgriva [62]3 years ago

4 0

Answer:

Step-by-step explanation:

$\text{We can notice:}$

$g(x)=6x^3-7,\ f(x)=(\underbrace{6x^3-7}_{g(x)})^3=\bigg(g(x)\bigg)^3$

$\text{If}\ f(x)=(h\circ g)(x)=h\bigg(g(x)\bigg),\ \text{then}\ h(x)=x^3$

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postnew [5]

12-3=9 they switch up and it still equals the same thing

5 0

2 years ago

Read 2 more answers

According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x^5

nata0808 [166]

Answer:

The correct option is A.

Step-by-step explanation:

The question is:

According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x5 – 2x4 + 9x3 – x2 + 12?

A).f(x) = 3x5 – 2x4 – 9x3 + x2 – 12

B).f(x) = 3x6 – 2x5 + 9x4 – x3 + 12x

C).f(x) = 12x5 – 2x4 + 9x3 – x2 + 3

D).f(x) = 12x5 – 8x4 + 36x3 – 4x2 + 48

Solution:

The function given to us is:

3x5 – 2x4 + 9x3 – x2 + 12

Find the factors of 12 and consider it as 'p'

The factors of 12 are:

p = +/- 1 , +/-2 , +/-3 , +/- 4 , +/-6

Now find the factors of 3 and consider it as 'q'

The factors of 3 are:

q = +/- 1 , +/- 3

We know that we write rational terms in p/q form.

Therefore the Rational roots are given by p/q

+/- 1 , +/-2 , +/-3 , +/- 4 , +/-6 , +/- 1/3 , +/- 2/3 , +/- 4/3

Now we will solve the first function given in part A.

f(x) = 3x^5 – 2x^4 - 9x^3 + x^2 - 12

Again find the factors of 12 and consider it as 'p'

The factors are:

p = +/- 1 , +/-2 , +/-3 , +/- 4 , +/-6

Now find the factors of 3 and consider it as 'q' .

q = +/- 1 , +/- 3

Rational root are given by p/q

+/- 1 , +/-2 , +/-3 , +/- 4 , +/-6 , +/- 1/3 , +/- 2/3 , +/- 4/3

Therefore the rational roots of the given function matches the rational roots of the given equation.

Hence the correct option is A

6 0

2 years ago

Jacob transformed quadrilateral FGHJ to F'G'H'J'.

Rudik [331]

Answer:

A. Reflection across the line x = 1

Step-by-step explanation:

Please find the attachment.

We have been given that Jacob transformed quadrilateral FGHJ to F'G'H'J'. We are asked to find which transformation Jacob used to reflect FGHJ to F'G'H'J'.

Since we know that while reflecting a figure, the line of reflection will lie between the original figure and reflected figure. Each point of the reflected figure will have the same distance from the line of reflection as the corresponding point of the original figure.

Now let us see our given choices one by one.

A. Reflection across the line x = 1.

Upon looking at point G and G' we can see that both points are equidistant (2 units) from the line x=1. Other corresponding points of both quadrilaterals are also equidistant from line x=1, therefore, Jacob used the reflection across the line x=1 to transform quadrilateral FGHJ to F'G'H'J'.

B. Reflection across the line y = 1 .

If Jacob had reflected quadrilateral across line y=1, the points of quadrilateral F'G'H'J' will lie in second and third quadrant. We can see from our graph that F'G'H'J' lies in 1st quadrant, therefore, option B is not a correct choice.

C. Reflection across the line y-axis.

If Jacob had reflected quadrilateral across y-axis, the coordinates of points of quadrilateral F'G'H'J' will be G'(1,4), H'(1,2), J'(4,0) and F'(2,5). Therefore, option B is not a correct choice.

D. Reflection across the x -axis.

If Jacob had reflected quadrilateral across x-axis, the points of quadrilateral F'G'H'J' will lie in third quadrant. We can see from our graph that F'G'H'J' lies in 1st quadrant, therefore, option D is not a correct choice.