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2 years ago

If f(x) = 1 - 2x^3, find the inverse of f.

1 answer:

7 0

Swap x and y's positions

f(x) is another way of saying y, so basically tha initial function is y = 1-2x^3.

Change it up to x = 1-2y^3 and solve for y

X - 1 = - 2y^3

(X - 1)/-2 = y^3

So the cube root of ((x-1)/2) = y

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Let f(x) = 1/x . Find the number b such that the average rate of change of f on the interval [2, b] is − 1/8

vekshin1

Answer:

b=4

Step-by-step explanation:

So, we have the function $f(x)=1/x$ . We need to find b such that the average rate of change or the slope is -1/8 between the intervel [2, b]. First, let's find f(2).

f(2) = 1/(2) = 1/2

So, we have the point (2, 1/2)

At point b, f(b) = 1/b.

Let's plug this into the slope formula:

$\frac{y_2-y_1}{x_2-x_1}=\frac{.5-\frac{1}{b} }{2-b} =-1/8$

Now, we just need to solve for b. First, let's multiply both the numerator and denominator by b (to get rid of the annoying fraction in the numerator).

$\frac{.5b-1}{2b-b^2} =\frac{-1}{8}$

Now, cross multiply.

$4b-8=b^2-2b$

$b^2-6b+8=0$

Solve for b. Factor using the numbers -4 and -2.

$=(b-4)(b-2)=0$

Thus, b=4 or b=2.

However, b=2 is not a possible solution since the interval [2,2] means nothing. Thus, b=4.

4 0

2 years ago

2. An online bookstore sells both print books and e-books (books in an electronic format). Customers can pay with either a gift

Fudgin [204]

Answer:

a.0.12

b. Dependent

Step-by-step explanation:

a. The two events mentioned here are " print book is purchases" and "customer using gift card". P(P)=0.6 and P(C)=0.2. we have to calculate the probability of print book selection for purchase and payment is made through gift card i.e. P(P∩C). P(P∩C)=P(P)*P(C)=0.6*0.2=0.12.

b. If P(A∩B)=P(A)*P(B), then the two events are independent. Here in the given situation two independent variables are "purchase of e-book" and "payment made using gift card"

P(E)=0.4

P(G)=0.2

P(E and G)=P(E∩G)=0.1

P(E)*P(G)=0.4*0.2=0.08 that is not equal to 0.1. So, the two events "e-book is purchased" and "Payment made by customer using gift card" are not independent.

5 0

3 years ago

What's the answer to this?

morpeh [17]

1: given 2: distributive property 3: multiplication property of equality 4: addition property of equality 5: division property of equality

5 0

2 years ago

Which percent is equivalent to 1/20

solmaris [256]

Answer:

Step-by-step explanation:

1/20 = 0.05

0.05 = 5%

3 0

2 years ago

Read 2 more answers

Avani wrote the linear equation y = 5 x + 4. Then, she wrote the equation of the line that is perpendicular to y = 5 x + 4 and t

Margarita [4]

Avani wrote the linear equation y = 5x + 4. Then, she wrote the equation of the line that is perpendicular to y = 5x+ 4 and that passes through (15,–2). If her new equation is in the form $y-\frac{1}{5}x+b$ , what is the value of b?

$\bf y=mx+b$

m is the slope
b is the y-intercept

The equation of a line that is perpendicular to another line always has the opposite reciprocal slope. In the original equation, the slope is 5. The opposite of 5, which refers to the sign, is -5. The reciprocal of -5 is -1/5. That means the slope of the new line is -1/5.

The perpendicular line: