All categories

3 years ago

For f(x) = 9x and g(x) = x + 3, find the following functions.

Mathematics

1 answer:

NeX [460]3 years ago

7 0

Answer:

a) 9*x + 27

b) 9*x+3

c) 45

d) 21

Step-by-step explanation:

since (f o g)(x) = f (g(x)) , then

a) (f o g)(x) = f (x + 3) = 9*(x+3) = 9*x + 27

similarly

b) (g o f)(x) = g (f(x)) = g ( 9x) = (9*x)+3 = 9*x+3

c) for x=2

(f o g)(2) = 9*2 + 27 = 45

d) for x=2

(g o f )(2) = 9*2 +3 = 21

thus we can see that the composition of functions is not necessarily commutative

You might be interested in

A person must score in the upper 8% of the population on an IQ test to qualify for membership in MENSA, the international high-I

Cloud [144]

Answer:

A person must get an IQ score of at least 138.885 to qualify.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 115, \sigma = 17$

(a). [7pts] What IQ score must a person get to qualify

Top 8%, so at least the 100-8 = 92th percentile.

Scores of X and higher, in which X is found when Z has a pvalue of 0.92. So X when Z = 1.405.

$Z = \frac{X - \mu}{\sigma}$

$1.405 = \frac{X - 115}{17}$

$X - 115 = 17*1.405$

$X = 138.885$

A person must get an IQ score of at least 138.885 to qualify.

5 0

3 years ago

Read 2 more answers

THe yearly profits of a company is $35,000, but they have been decreasing 6% per year. What will be the profit in 8 years?

Elenna [48]

Answer:

The total money will be $113750(I think)

Just check other's answers.(or use a calculator.)

7 0

3 years ago

When plotted on a grid, the paths between four neighborhood houses form the shape of a kite as shown.

KatRina [158]

Answer:

The area of the figure is 1,000 square feet

Step-by-step explanation:

we know that

The area of the kite ABCD

is equal to

$A=\frac{1}{2}[AC*BD]$

where

AC and BD are the diagonals of the kite

we have

$BD=50\ ft\\AC=40\ ft$

substitute

$A=\frac{1}{2}[40*50]=1,000\ ft^2$

3 0

3 years ago

115 is what percent of 200?

Valentin [98]

57.5 is the answer. Because think of 200 as 100% and 15 out of a hundered is ______. Right.

4 0

3 years ago

What is the solution to this equation 2/3x+1=1/6×-7

Alika [10]

Answer:

A . x= -16

Step-by-step explanation:

$\\\frac{2}{3}x+1=\frac{1}{6}x-7\\\\\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\\\\frac{2}{3}x+1-1=\frac{1}{6}x-7-1\\\\\frac{2}{3}x=\frac{1}{6}x-8\\\\\mathrm{Subtract\:}\frac{1}{6}x\mathrm{\:from\:both\:sides}\\\\\frac{2}{3}x-\frac{1}{6}x=\frac{1}{6}x-8-\frac{1}{6}x\\\\= \frac{1}{2}x=-8\\\\\mathrm{Multiply\:both\:sides\:by\:2}\\\\2\times \frac{1}{2}x=2\left(-8\right)\\\\x=-16$

7 0

3 years ago