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3 years ago

If f(x) = 2x - 4 and g(x)= x², what is f(g(x))?

Mathematics

1 answer:

kupik [55]3 years ago

6 0

Answer:

Step-by-step explanation:

To evaluate f(g(x)) substitute x = g(x) into f(x)

f(g(x))

= f(x²)

= 2(x²) - 4 = 2x² - 4

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Parameterize $C$ by

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where $0\le t\le\pi$ . Then the line integral is

$\displaystyle\int_Cx^2y\,\mathrm dS=\int_{t=0}^{t=\pi}x(t)^2y(t)\left\|\frac{\mathrm d\mathbf r(t)}{\mathrm dt}\right\|\,\mathrm dt$
$=\displaystyle\int_{t=0}^{t=\pi}(3\cos t)^2(3\sin t)\sqrt{(-3\sin t)^2+(3\cos t)^2}\,\mathrm dt$
$=\displaystyle3^4\int_{t=0}^{t=\pi}\cos^2t\sin t\,\mathrm dt$

Take $u=\cos t$ , then

$=\displaystyle-3^4\int_{u=1}^{u=-1}u^2\,\mathrm du$
$=\displaystyle3^4\int_{u=-1}^{u=1}u^2\,\mathrm du$
$=\displaystyle2\times3^4\int_{u=0}^{u=1}u^2\,\mathrm du$
$=54$

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Answer:

Step-by-step explanation:

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Step-by-step explanation:

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