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2 years ago

Given that f(x) = 4x√3x + 3 and g(x) = 2√x+1, find (f/g)(x)

Mathematics

1 answer:

Tresset [83]2 years ago

8 0

Answer:

$2x\sqrt{3}.$

Step-by-step explanation:

$\frac{f}{g}(x)=\frac{4x\sqrt{3x+3}}{2\sqrt{x+1}}=\frac{2*2*x*\sqrt{3}*\sqrt{x+1}}{2*\sqrt{x+1}}=2x\sqrt{3}.$

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Evaluate each expression for the given values of the variables: |a+x|/2-|a-x|/2if a=−2; x=−6

jok3333 [9.3K]

Answer:

Step-by-step explanation:

|a+x|/2-|a-x|/2

Plug in the values.

|-2+-6|/2-|-2- -6|/2

Evaluate.

|-8|/2-|4|/2

Apply rule : |-a| = a

8/2 - 4/2

4 - 2

Subtract.

= 2

3 0

3 years ago

Read 2 more answers

F(x) = 3x + x3

____ [38]

Answer:

Please check the explanation.

Step-by-step explanation:

Given

f(x) = 3x + x³

Taking differentiate

$\frac{d}{dx}\left(3x+x^3\right)$

$\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'$

$=\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(x^3\right)$

solving

$\frac{d}{dx}\left(3x\right)$

$\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'$

$=3\frac{d}{dx}\left(x\right)$

$\mathrm{Apply\:the\:common\:derivative}:\quad \frac{d}{dx}\left(x\right)=1$

$=3\cdot \:1$

$=3$

now solving

$\frac{d}{dx}\left(x^3\right)$

$\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}$

$=3x^{3-1}$

$=3x^2$

Thus, the expression becomes

$\frac{d}{dx}\left(3x+x^3\right)=\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(x^3\right)$

$=3+3x^2$

Thus,

f'(x) = 3 + 3x²

Given that f'(x) = 15

substituting the value f'(x) = 15 in f'(x) = 3 + 3x²

f'(x) = 3 + 3x²

15 = 3 + 3x²

switch sides

3 + 3x² = 15

3x² = 15-3

3x² = 12

Divide both sides by 3

x² = 4

$\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

$x=\sqrt{4},\:x=-\sqrt{4}$

$x=2,\:x=-2$

Thus, the value of x will be:

$x=2,\:x=-2$

5 0

3 years ago

Charles has read 180 pages of a book this is 3/4 of the total number of pages in the book If P represents the number of pages in

KengaRu [80]

The answer is 240 :3

60+60= 120
120+60 = 180
and 60 more would be 240

60 fours would be 240
3 60's would be 180. So your answer is 240

4 0

3 years ago

Read 2 more answers

What is the vale of ■ in this equation?<br>7×9=(7×10)-(7×■)

aliina [53]

The answer is 1 because 7*9 is 63
7*10=70 70-7=63

5 0

3 years ago

Read 2 more answers

Please help me i’ll give brainliest

liraira [26]

Answer:

105 degrees

Step-by-step explanation:

You need to understand the properties of corresponding angles and supplementary angles.

6 0

3 years ago