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Question

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

Let f1:RR,f2:[0,]R,f3:RR and f4:R[0,) be defined by f1(x)={|x|,if x<0ex,if x0f2(x)=x2;f3(x)={sinx,if x<0x, if x0 and f4(x)={f2[f1(x)], if x<0f2[f1(x)]1, if x0
Column 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
 


  1. A-r    B-p    C-s    D-q

  2. A-p    B-r    C-s    D-q

  3. A-r    B-p    C-q    D-s

  4. A-p    B-r    C-q    D-s


Solution

The correct option is D

A-p    B-r    C-q    D-s


f1(x)={x, x<0ex, x0
f2(x)=x2, x0
f3(x)={sin x, x<0x, x0
f4(x)={f2(f1(x)), x<0f2(f(x))1, x0
Now, f2(f1(x))={x2, x<0e2x, x0
f4={x2, x<0e2x1, x0
As f4(x) is continuous, f4(x)={2x, x<02e2x, x>0

f;4(0) is not defined. Its range is [0,).
Thus, range = coadmin = [0,), thus f4 is onto.
Also, horizontal line(drawn parallel to X-axis) meets the curve more than once, thus function is not one-one.

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