(i will give 30 points)
for the function f(x) = (8-­2x)2 ,find f-­1 . determine whether f­-1 is a function.

answer choices:
f­-1(x) = ±8+x2−−−√; f­-1 is a function

f­-1(x) = ±8+x2−−−√; f­-1 is not a function

f­-1(x) = 8±x√2; f­-1 is not a function

f­-1(x) = 8±x√2; f­-1 is a function

4 ± 1/2sqrt(x) = y

This is not a function

Step-by-step explanation:

f(x) = (8-2x)^2

y = (8-2x)^2

To find the inverse function, exchange x and y and then solve for y

x = (8-2y)^2

Take the square root of each side

±sqrt(x) = 8-2y

Subtract 8 from each side

-8±sqrt(x) = 8-8-2y

-8±sqrt(x) = -2y

Divide by -2

-8/-2±  1/2sqrt(x) = -2/-2y

4 ± 1/2sqrt(x) = y

This is not a function

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places