Let f: R → R be a function defined as f(x)= {5, if x ≤ 1; a + b x, if 1<x<3; b +5 x, if 3 ≤ x<5; 30, if x ≥ 5} Then, f is:

Let $\displaystyle f: \mathbf{R} \rightarrow \mathbf{R}$ be a function defined as $$f(x)=\left\{\begin{array}{rlr} 5, & \text { if } & x \leq 1 \\ \mathrm{a}+\mathrm{b} x, & \text { if } & 1<x<3 \\ \mathrm{~b}+5 x, & \text { if } & 3 \leq x<5 \\ 30, & \text { if } & x \geqslant 5 \end{array}\right. $$ Then, $\displaystyle f$ is :