Let `fa n dg` be increasing and decreasing functions, respectively, from `[0,oo]to[0,oo]dot` Let `h(x)=f(g(x))dot` If `h(0)=0,` then `h(x)-h(1)` is (a)always zero (b) always negative always positive (d) strictly increasing none of these

Options

A. always 0
B. always positive
C. always negative
D. strictly increasing

Answer

A

Explanation

since composition of an increasing function and a decreasing function is always a decreasing fuction .Therefore h(x)` [ 0, oo) rarr [0,oo)`is a decreasing function .
`h(x) le 0 for all x le 0`
`rArr h(x) =0 for all x ge 0 " "[{:(because h(x)in [0","oo)),(rArr h(x) ge 0 for all x in [0","oo)):}]`