The function f is defined by f ( x ) = 25 x + 30 .

Choice C is correct. It’s given that the function $f$ is defined by $f\left(x\right)=25x+30$. Substituting $2$ for $x$ in this equation yields $f\left(2\right)=25\left(2\right)+30$, which is equivalent to $f\left(2\right)=50+30$, or $f\left(2\right)=80$. Therefore, the value of $f\left(x\right)$ is $80$ when $x=2$.

Choice A is incorrect. This is the value of $25\left(2\right)$, not $25\left(2\right)+30$.

Choice B is incorrect. This is the value of $25+2+30$, not $25\left(2\right)+30$.

Choice D is incorrect. This is the value of $\left(25+30\right)\left(2\right)$, not $25\left(2\right)+30$.