JEE Advanced 2014 Paper 1 Mathematics Q5

Mathematics

Problem

Let

f:[a,b]\to[1,\infty)

be a continuous function and let

g:\mathbb R\to\mathbb R

be defined as

g(x)=\begin{cases}0,&x<a,\\ \displaystyle\int_a^x f(t)\,dt,&a\leq x\leq b,\\ \displaystyle\int_a^b f(t)\,dt,&x>b.\end{cases}

Then