The function f is defined by f x = 4 x - 1 . What is

Choice C is correct. It’s given that function $f$ is defined by the equation $f\left(x\right)=4x^{-1}$. The value of $f\left(21\right)$ is the value of $f\left(x\right)$ when $x=21$. Substituting $21$ for $x$ in the given equation yields $f\left(21\right)=4{\left(21\right)}^{-1}$, which is equivalent to $f\left(21\right)=4\left(\frac{1}{21}\right)$, or $f\left(21\right)=\frac{4}{21}$.

Choice A is incorrect. This is the value of $f\left(21\right)$ when $f\left(x\right)=-4x$, rather than $f\left(x\right)=4x^{-1}$.

Choice B is incorrect. This is the value of $f\left(21\right)$ when $f\left(x\right)={\left(4x\right)}^{-1}$, rather than $f\left(x\right)=4x^{-1}$.

Choice D is incorrect. This is the value of $f\left(21\right)$ when $f\left(x\right)=\left(4^{-1}\right)x$, rather than $f\left(x\right)=4x^{-1}$.