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4 years ago

If f(x) = 6x +5 and g(x) = 2x – 7 find (fºg)(x)

Mathematics

1 answer:

adell [148]4 years ago

7 0

Answer:

f(g(x)) = 12x - 37

Step-by-step explanation:

Step 1: Define

f(x) = 6x + 5

g(x) = 2x - 7

Step 2: Find f(g(x))

f(g(x)) = 6(2x - 7) + 5

f(g(x)) = 12x - 42 + 5

f(g(x)) = 12x - 37

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What are some good note for Notes for Median and mean

dexar [7]

Answer:

To find the Median arrange the data in order from least to greatest then find the middle number. To find the middle number cross of one from the front and one from the bcak. If there are 2 numbers left in the middle add those numbers together and them divided the sum by 2.

The mean is the average of the numbers. It is easy to find. First, add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.

Step-by-step explanation:

8 0

3 years ago

The density of gold is 19.3 g/cm3. What is the density in kilograms per cubic meter? A. 1.93 x 102 kg/m3 B. 1.93 x 104 kg/m3 C.

never [62]

we are given

density of gold = 19.3g/cm^3

we know that

$1g=10^{-3}kg$

$1cm=10^{-2}m$

we have to change it into kg/m^3

so, we can plug these values

$19.3\frac{g}{cm^3} =19.3\frac{10^{-3}kg}{(10^{-2}m)^3}$

we can also write as

$19.3\frac{g}{cm^3} =19.3\frac{10^{-3}}{(10^{-2})^3}\frac{kg}{m^3}$

now, we can simplify it

$19.3\frac{g}{cm^3} =19300\frac{kg}{m^3}$

$19.3\frac{g}{cm^3} =1.93\times 10^4 \frac{kg}{m^3}$ ..............Answer

3 0

3 years ago

Geometry help please

Law Incorporation [45]

<h3>Answer: RJ = 10</h3>

=======================================================

Explanation:

Recall that midsegments are half as long as the side they are parallel to. In this case, midsegment PQ is parallel to segment GJ. This means PQ is half as long as GJ. Phrased another way, we can say GJ is twice as long as PQ.

So,

GJ = 2*PQ

Also, we can see that GR = RJ due to the triple tickmarks they share. This leads to GJ = GR+RJ = RJ+RJ = 2*RJ

Or in short,

GJ = 2*RJ

---------

In summary we can see that

GJ = 2RJ
GJ = 2PQ

equating both right hand sides leads to

2RJ = 2PQ

RJ = PQ

Because PQ is 10 units, this means RJ is also 10 units.

--------------------

Another way to see why PQ = RJ is to notice how triangles HPQ and QRJ are congruent triangles (use SAS to prove this). The corresponding pieces PQ and RJ are the same length, so PQ = RJ = 10.

3 0

3 years ago

PLEASE HELP!!!!<br> Which of these pair of functions are inverse functions?

Mamont248 [21]

Answer:

Option B and C are correct.

Step-by-step explanation:

Inverse function: If both the domain and the range are R for a function f(x), and if f(x) has an inverse g(x) then:

$f(g(x)) = g(f(x)) = x$ for every x∈R.

Let $f(x) = \frac{1}{2}(\ln(\frac{x}{2}) -1)$ and $g(x) = 2e^{2x+1}$

Use logarithmic rules:

$ln e^a = a$

$e^{lnx} = x$

$\ln a^b = b\ln a$

then, by definition;

$f(g(x)) = f(2e^{2x+1}) =\frac{1}{2}(\ln(\frac{2e^{2x+1}}{2})-1)$ = $\frac{1}{2}(\ln(e^{2x+1}}){-1) = \frac{1}{2} (2x+1-1) =\frac{1}{2}(2x) = x$

$g(f(x)) = g(\frac{1}{2}(\ln(\frac{x}{2}) -1)) = 2e^{2({\frac{1}{2}(\ln(\frac{x}{2}) -1})+1$ $2e^{(\ln(\frac{x}{2}) -1+1}=2e^{\ln(\frac{x}{2})} =2\cdot \frac{x}{2} = x$

Similarly;

for $f(x) = \frac{4 \ln(x^2)}{e^2}$ and $g(x) = e^{\frac{e^2 \cdot x}{8} }$

then, by definition;

$f(g(x)) = f(e^{\frac{e^2 \cdot x}{8}}) =\frac{4 \ln {(\frac{e^2 \cdot x}{8})^2}}{e^2}$ = $\frac{8 \ln {(\frac{e^2 \cdot x}{8})}}{e^2} =\frac{8\frac{e^2\cdot x}{8} }{e^2}=\frac{8e^2 \cdot x}{8e^2}=x$

Similarly,

g(f(x)) = x

Therefore, the only option B and C are correct. As the pairs of functions are inverse function.

3 0

3 years ago

Solve the following proportion for x 3/8 =x/13

zhenek [66]

The value of x in the proportion is x = 39/8

<h3>How to solve the proportion?</h3>

The proportion is given as:

3/8 =x/13

Cross multiply

8 * x = 3 * 13

Evaluate

8x = 39

Divide by 8

x = 39/8

Hence, the value of x in the proportion is x = 39/8

Read more about proportions at:brainly.com/question/1781657

#SPJ1

7 0

2 years ago