Question(s) from Search: IIT

A function f : ℝ → ℝ, where ℝ is the set of real numbers, is defined by . Find the interval of values of α for which f is onto. Is the function one to one for α= 3? Justify your answer.

Let f : ℝ → ℝ be a function defined by $f\left(x\right)=\{\begin{array}{cc}[x]& x\le 2\\ 0& x>2\end{array}$

where [x] denotes the greatest integer less than or equal to x. If $I=\underset{-1}{\overset{2}{\int }}\frac{\mathrm{xf}\left(x^2\right)}{2+f(x+1)}\mathrm{dx}$ then the value of (4I – 1) is

a) 1

b) 3

c) 2

d) 0