The function f is defined by f ( x ) = 4 x - 3 .

Choice B is correct. It’s given that the function $f$ is defined by $f\left(x\right)=4x-3$. Substituting $10$ for $x$ in the given function yields $f\left(10\right)=4\left(10\right)-3$, which is equivalent to $f\left(10\right)=40-3$, or $f\left(10\right)=37$. Therefore, the value of $f\left(10\right)$ is $37$.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect. This is the value of $f\left(10\right)$ for the function $f\left(x\right)=4x$, not $f\left(x\right)=4x-3$.

Choice D is incorrect. This is the value of $f\left(10\right)$ for the function $f\left(x\right)=4x+3$, not $f\left(x\right)=4x-3$.