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3 years ago

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

Mathematics

1 answer:

nadya68 [22]3 years ago

4 0

Answer: $h(x)=x-2$

Step-by-step explanation:

To find the inverse of the function $f(x) = x + 2$ , the first step is to replace f(x) with "y":

$f(x) =y= x + 2\\\\ y = x + 2$

The second step is to solve for the variable "x":

$x=y-2$

The third step is to interchange the variables, then:

$y=x-2$

Finally, let be h(x) the inverse of the function f(x). Then, you can replace "y" with h(x). Therefore, this is:

$h(x)=x-2$

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Simplify the expression shown below: (a^3b^12c^2)^2(a^5c^2)^3(b^5c^4)^0

NemiM [27]

= a^21b^24c^10
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3 years ago

The total monthly profit for a firm is P(x)=6400x−18x^2− (1/3)x^3−40000 dollars, where x is the number of units sold. A maximum

wlad13 [49]

Answer:

Maximum profits are earned when x = 64 that is when 64 units are sold.

Maximum Profit = P(64) = 2,08,490.666667$

Step-by-step explanation:

We are given the following information: $P(x) = 6400x - 18x^2 - \frac{x^3}{3} - 40000$ , where P(x) is the profit function.

We will use double derivative test to find maximum profit.

Differentiating P(x) with respect to x and equating to zero, we get,

$\displaystyle\frac{d(P(x))}{dx} = 6400 - 36x - x^2$

Equating it to zero we get,

$x^2 + 36x - 6400 = 0$

We use the quadratic formula to find the values of x:

$x = \displaystyle\frac{-b \pm \sqrt{b^2 - 4ac} }{2a}$ , where a, b and c are coefficients of $x^2, x^1 , x^0$ respectively.

Putting these value we get x = -100, 64

Now, again differentiating

$\displaystyle\frac{d^2(P(x))}{dx^2} = -36 - 2x$

At x = 64, $\displaystyle\frac{d^2(P(x))}{dx^2} < 0$

Hence, maxima occurs at x = 64.

Therefore, maximum profits are earned when x = 64 that is when 64 units are sold.

Maximum Profit = P(64) = 2,08,490.666667$

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3 years ago

Acone has a height of 7 ft and a radius of 4 ft. Which equation can find the volume of the cone?

Marina86 [1]

Answer:

Volume of the cone = $117.06\,feet^3$

Step-by-step explanation:

Height of the cone = $7\,feet$

Radius of the cone = $4\,feet$

Volume of a cone is:

$\pi \times r^2\times \dfrac{h}{3}$

As, $\pi =\dfrac{22}{7} =3.14$

Volume is:

$=3.14\times(4\times 4)\times \dfrac{7}{3}\\\\ =3.14\times 16 \times 2.33\\\\=3.14\times 37.28\\\\=117.06\,feet^3$

The volume of the cone is: $117.06\,feet^3$

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3 years ago

The surface area of a rectangular prism with length l, width w, and height h is given by the expression 2lw+2lh+2wh. Write an eq

Yuki888 [10]

Answer:

2(lw+lh+wh)

Step-by-step explanation:

2(lw+lh+wh) using distributive property

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3 years ago

Which expression converts 100inches per minute to feet per minute?

Rzqust [24]

The are 12 inches in a foot. So 100ipm ÷12= fpm :) hope this helps

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4 years ago