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AleksandrR [38]
3 years ago
7

If h(x) = (f o g)(x) and h(x) = ∛7x+1, find f(x) and g(x)

Mathematics
1 answer:
Mariana [72]3 years ago
7 0
There's more than one way to combine them really
but an obvious one will be

\bf \begin{array}{llll}
h(x)&=&(f\circ g)(x)\\\\
&&\sqrt[3]{7x+1}\\\\
&&\sqrt[3]{g(x)}\leftarrow 
\begin{array}{llll}
f(x)=\sqrt[3]{x }\\\\
g(x)=7x+1
\end{array}
\end{array}\\\\
-----------------------------\\\\
(f\circ g)(x)\iff f[\quad g(x)\quad ]=\sqrt[3]{g(x)}\implies  f[\quad g(x)\quad ]=\sqrt[3]{7x+1}
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Let f be a differentiable function such that f(1)=π and f'(x)=√x^3+6. what is the value of f(5)?
natali 33 [55]

The value of f(5) is 49.1

Step-by-step explanation:

To find f(x) from f'(x) use the integration

f(x) = ∫ f'(x)

1. Find The integration of f'(x) with the constant term

2. Substitute x by 1 and f(x) by π to find the constant term

3. Write the differential function f(x) and substitute x by 5 to find f(5)

∵ f'(x) = \sqrt{x^{3}} + 6

- Change the root to fraction power

∵ \sqrt{x^{3}} = x^{\frac{3}{2}}

∴ f'(x) = x^{\frac{3}{2}} + 6

∴ f(x) = ∫ x^{\frac{3}{2}} + 6

- In integration add the power by 1 and divide the coefficient by the

 new power and insert x with the constant term

∴ f(x) = \frac{x^{\frac{5}{2}}}{\frac{5}{2}} + 6x + c

- c is the constant of integration

∵ \frac{x^{\frac{5}{2}}}{\frac{5}{2}}=\frac{2}{5}x^{\frac{5}{2}}

∴ f(x) = \frac{2}{5} x^{\frac{5}{2}} + 6x + c

- To find c substitute x by 1 and f(x) by π

∴ π = \frac{2}{5} (1)^{\frac{5}{2}} + 6(1) + c

∴ π = \frac{2}{5} + 6 + c

∴ π = 6.4 + c

- Subtract 6.4 from both sides

∴ c = - 3.2584

∴ f(x) = \frac{2}{5} x^{\frac{5}{2}} + 6x - 3.2584

To find f(5) Substitute x by 5

∵ x = 5

∴ f(5) = \frac{2}{5} (5)^{\frac{5}{2}} + 6(5) - 3.2584

∴ f(5) = 49.1

The value of f(5) is 49.1

Learn more:

You can learn more about differentiation in brainly.com/question/4279146

#LearnwithBrainly

4 0
3 years ago
Please help! I need an answer fast!
Rashid [163]
<u><em>To find the answer,Divide 20 by 5 and you get</em></u>
<u><em>C.4.8
Good luck!
</em></u>
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3 years ago
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seraphim [82]

5400

4500 multiplied by 1.2

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Solve for y:<br><br> 9y = 36<br><br> A) y=4<br><br> B)y=12<br><br> C)y=18 <br><br> D) y=9
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Answer:

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Step-by-step explanation:

9y=36

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y=4

Now test that it is correct by replacing y with 4

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