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3 years ago

6

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

1 answer:

weeeeeb [17]3 years ago

4 0

Answer:

Hello,

Step-by-step explanation:

$f(x)=\dfrac{4}{x} \\\\g(x)=\dfrac{4}{x} \\\\\\(gof)(x)=f(g(x))=f(\dfrac{4}{x} )=\dfrac{4}{\dfrac{4}{x} } =\dfrac{4*x}{4} =x\\\\\\(fog)(x)=g(f(x))=g(\dfrac{4}{x} )=\dfrac{4}{\dfrac{4}{x} } =\dfrac{4*x}{4} =x\\$

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The general solution of 2 y ln(x)y' = (y^2 + 4)/x is

Sav [38]

Replace $y'$ with $\dfrac{\mathrm dy}{\mathrm dx}$ to see that this ODE is separable:

$2y\ln x\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{y^2+4}x\implies\dfrac{2y}{y^2+4}\,\mathrm dy=\dfrac{\mathrm dx}{x\ln x}$

Integrate both sides; on the left, set $u=y^2+4$ so that $\mathrm du=2y\,\mathrm dy$ ; on the right, set $v=\ln x$ so that $\mathrm dv=\dfrac{\mathrm dx}x$ . Then

$\displaystyle\int\frac{2y}{y^2+4}\,\mathrm dy=\int\dfrac{\mathrm dx}{x\ln x}\iff\int\frac{\mathrm du}u=\int\dfrac{\mathrm dv}v$

$\implies\ln|u|=\ln|v|+C$

$\implies\ln(y^2+4)=\ln|\ln x|+C$

$\implies y^2+4=e^{\ln|\ln x|+C}$

$\implies y^2=C|\ln x|-4$

$\implies y=\pm\sqrt{C|\ln x|-4}$

4 0

3 years ago

Frank started an assignment at 6:26 PM and finished it at 7:44 PM. How long did it take him? Give your answer in minutes.

Svet_ta [14]

7.44-6.26=1.18
1.18 in minutes is 78 minutes bc 1 hour is 60 minutes + 18 minutes is 78
Hope this helps :D

5 0

2 years ago

Read 2 more answers

Which of the following are independent variables?

Lapatulllka [165]

Answer:

i think that it is oil

Step-by-step explanation:

because it does not change

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3 years ago

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Harry earns an hourly rate of $15. For each additional hour over 40 hours, he earns 150% percent of his regular hourly rate. Las

irinina [24]

Answer:

51 hours

Step-by-step explanation:

$15 x 40 = $600

$15 x 1.50 = $22.5

$22.5 x 11 = $247.5

$600 + $247.5 = $847.5

40 + 11 = 51 hours

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150% of what number is 34

Svetradugi [14.3K]

150% of 51 is 34. So your answer is 51

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