Match the conditions/expressions in Column I with statement in Column II.Let f1:R→R,f2:[0,∞]→R,f3:R→R and f4:R→[0,∞) be defined by f1(x)={|x|,if x<0ex,if x≥0f2(x)=x2;f3(x)={sinx,if x<0x, if x≥0 and f4(x)={f2[f1(x)], if x<0f2[f1(x)]−1, if x≥0Column IColumn IIa.f4 isp.onto but not one-oneb.f3 isq.neither continuous nor one-onec.f2off1 isr.differentiable but not one-oned.f2 iss.continuous and one-one

Match the conditions/expressions in Column I with statement in Column

1.	Match the conditions/expressions in Column I with statement in Column II.Let f1:R→R,f2:[0,∞]→R,f3:R→R and f4:R→[0,∞) be defined by f1(x)={\|x\|,if x<0ex,if x≥0f2(x)=x2;f3(x)={sinx,if x<0x, if x≥0 and f4(x)={f2[f1(x)], if x<0f2[f1(x)]−1, if x≥0Column IColumn IIa.f4 isp.onto but not one-oneb.f3 isq.neither continuous nor one-onec.f2off1 isr.differentiable but not one-oned.f2 iss.continuous and one-one
Answer» Match the conditions/expressions in Column I with statement in Column II. Let $f_{1} : R \to R, f_{2} : [0, \infty] \to R, f_{3} : R \to R$ and $f_{4} : R \to [0, \infty)$ be defined by $f_{1} (x) = {\begin{matrix} \| x \|, i f x < 0 e^{x}, i f x \geq 0 \end{matrix} f_{2} (x) = x^{2}; f_{3} (x) = {\begin{matrix} s i n x, i f x < 0 x, i f x \geq 0 \end{matrix}$ and $f_{4} (x) = {\begin{matrix} f_{2} [f_{1} (x)], i f x < 0 f_{2} [f_{1} (x)] - 1, i f x \geq 0 \end{matrix}$ $\begin{matrix} Column I & Column II a . f_{4} i s & p . onto but not one-one b . f_{3} i s & q . neither continuous nor one-one c . f_{2} o f f_{1} i s & r . differentiable but not one-one d . f_{2} i s & s . continuous and one-one \end{matrix}$