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Math·Advanced Math·Nonlinear equations in one variable and systems of equations in two variables

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$f(x)=\sqrt{3x+8}$

The function $f$ is defined by the given equation. If $f(a)=-9a$, where $a$ is a constant, what is the value of $a$?

A

$\frac{1}{3}$

B

$\frac{8}{27}$

C

$-\frac{8}{27}$

D

$-\frac{1}{3}$