9)

1. determine if the functions are inverse functions

kirill115 [55]

Answer:

Question 1

The function $f(x) = x + 6$ is one-to-one, so it does have an inverse.

The inverse of +6 is -6, so $f^{-1}(x)=x-6$

Therefore, g(x) is the inverse of f(x).

Question 2

The function $f(x) = -3x -9$ is one-to-one, so it does have an inverse.

To find the inverse, replace f(x) with y:

$\implies y = -3x -9$

Rearrange the equation to make x the subject:

$\implies y+9= -3x$

$\implies x=-\dfrac13(y+9)$

$\implies x=-\dfrac13y-3$

Replace x with $f^{-1}(x)$ and y with x:

$\implies f^{-1}(x)=-\dfrac13x-3$

Therefore, g(x) is the inverse of f(x).

5 0

2 years ago

Evaluate the Expression When X=2, 3x-1=

Alex777 [14]

Answer:

5

Step-by-step explanation:

If X equals 2, then 3 times X would be 6. This is because if a number and a variable are put together, you have to multiply them. 6-1 is 5.

4 0

3 years ago

The distribution of the average amount of sleep per night gotten by college students is roughly bell-shaped with mean 412 minute

kirza4 [7]

Answer:

$P(X$

$P(z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(412,68)$