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

hard

$$f(x)=\sqrt{6x+7}$$

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

$-\frac{7}{27}$

C

$\frac{7}{27}$

D

$\frac{1}{3}$