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3 years ago

Consider the functions f(x) = x2 − 13 and g(x) = x + 5. What is the value of f[g(−4)]? (5 points)

Mathematics

1 answer:

sergejj [24]3 years ago

5 0

It would be a because g(-4) is the same as g(x)= -4+5, which equals 1. f(1)=1^2-13, which means f(1) is -12.

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3 years ago

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3 years ago

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tankabanditka [31]

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$\displaystyle \int \frac{t^2}{1 - 3t} \, dt = -\frac19 \int \left(3t + 1 - \frac1{1-3t}\right) \, dt \\\\ = -\frac19 \left(\frac32 t^2 + t + \frac13 \ln|1 - 3t|\right) + C \\\\ = \boxed{-\frac{t^2}6 - \frac t9 - \frac{\ln|1-3t|}{27} + C}$

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$\displaystyle \int x^n \, dx = \frac{x^{n+1}}{n+1} + C ~~~~ (n\neq-1)$

and a substitution to integrate the last term,

$\displaystyle \int \frac{dt}{1-3t} = -\frac13 \int \frac{du}u \\\\ = -\frac13 \ln|u| + C \\\\ = -\frac13 \ln|1-3t| + C ~~~ (u=1-3t \text{ and } du = -3\,dt)$

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using the same approach as above.

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2 years ago