All categories

3 years ago

What is the inverse of the function g(x) = x^3/8 + 16 ?

Mathematics

1 answer:

lesya692 [45]3 years ago

6 0

Answer:

$\hookrightarrow \: { \rm{f(x) = \frac{ {x}^{3} }{8} + 16}} \\$

• let f(x) be m:

${ \rm{m = \frac{ {x}^{3} }{8} + 16}} \\$

• make x the subject of the function:

${ \rm{8m = {x}^{3} + 128}} \\ \\ { \rm{ {x}^{3} = 8m - 128 }} \\ \\ { \rm{ {x}^{3} = 8(m - 16) }} \\ \\ { \rm{x = \sqrt[3]{8} \times \sqrt[3]{(m - 16)} }} \\ \\ { \rm{x = 2 \sqrt[3]{(m - 16)} }}$

• therefore:

${ \boxed{ \rm{ {f}^{ - 1} (x) = 2 {(m - 16)}^{ \frac{1}{3} } }} }\\$

You might be interested in

A company sells kitchen toys for kids, including artificial carrots that are cone shaped with a radius of 1 cm and a height of 6

sdas [7]

Answer:

Total space in the box is 75.2 cm³.

Step-by-step explanation:

Cone:

It is three dimension shape.
It has a vertex.
The slant height of a cone $l^2=r^2+h^2$ , $l$ = slant height, r= radius of the base, h= height
The lateral surface area is πrl
The volume of a cone is $\frac13 \pi r^2h$ .

The artificial carrot that are cone shaped with a radius 1 cm and a height of 6 cm.

So, the volume of the cone is = $\frac13 \pi r^2h$

$=\frac13 \pi (1)^2.6$

$=2\pi$ cm³

The volume 1 dozen carrots is = (12×2π) cm³

=75.4 cm³

The volume of the box= The volume of the 1 dozen carrot.

Total space in the box is 75.2 cm³.

4 0

3 years ago

F⃗ (x,y)=−yi⃗ +xj⃗ f→(x,y)=−yi→+xj→ and cc is the line segment from point p=(5,0)p=(5,0) to q=(0,2)q=(0,2). (a) find a vector pa

DerKrebs [107]

a. Parameterize $C$ by

$\vec r(t)=(1-t)(5\,\vec\imath)+t(2\,\vec\jmath)=(5-5t)\,\vec\imath+2t\,\vec\jmath$

with $0\le t\le1$ .

b/c. The line integral of $\vec F(x,y)=-y\,\vec\imath+x\,\vec\jmath$ over $C$ is

$\displaystyle\int_C\vec F(x,y)\cdot\mathrm d\vec r=\int_0^1\vec F(x(t),y(t))\cdot\frac{\mathrm d\vec r(t)}{\mathrm dt}\,\mathrm dt$

$=\displaystyle\int_0^1(-2t\,\vec\imath+(5-5t)\,\vec\jmath)\cdot(-5\,\vec\imath+2\,\vec\jmath)\,\mathrm dt$

$=\displaystyle\int_0^1(10t+(10-10t))\,\mathrm dt$

$=\displaystyle10\int_0^1\mathrm dt=\boxed{10}$

d. Notice that we can write the line integral as

$\displaystyle\int_C\vecF\cdot\mathrm d\vec r=\int_C(-y\,\mathrm dx+x\,\mathrm dy)$

By Green's theorem, the line integral is equivalent to

$\displaystyle\iint_D\left(\frac{\partial x}{\partial x}-\frac{\partial(-y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=2\iint_D\mathrm dx\,\mathrm dy$

where $D$ is the triangle bounded by $C$ , and this integral is simply twice the area of $D$ . $D$ is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.

4 0

3 years ago

Neal used magnetic letters to spell the word communication on his file cabinet. One of the magnets fell on the floor. What is th

Nataliya [291]

Answer:

the likehood that an n fell on the floor is 2 in 13.

Step-by-step explanation:

8 0

4 years ago

Read 2 more answers

How does the graph of y=-3√2x-4 compare to the graph of y=-3√x-4?

kifflom [539]

Assuming the graph is y=-3(√2x)-4 and y=-3√(x-4) the transformation would be:

The graph is compressed horizontally by a factor of 2
x=1/2x'
y=-3(√2x)-4
y=-3(√x')-4 

moved left 4
x=x'-4
y=-3(√x)-4
y=-3(√x'-4)-4

moved down 4
y=y'-4
y=-3(√x-4)-4
y'-4=-3(√x'-4)-4
y'=-3(√x'-4)-4 +4
y'=-3(√x'-4)

Answer: C. The graph is compressed horizontally by a factor of 2, moved left 4, and moved down 4.

6 0

4 years ago

Read 2 more answers

What expression using gcf 14xy+8yz

salantis [7]

Answer:

2y(7x + 4z)

Step-by-step explanation:

Consider the common factors of both terms

The gcf of 14 and 8 is 2

The gcf of xy and yz is y

Thus the gcf of both terms is 2y, thus

14xy + 8yz

= 2y(7x + 4z)

6 0

3 years ago

Read 2 more answers