Question
Question: Let f & g be increasing and decreasing function respectively from [0, ∞) to [0, ∞). Let h(x) = f(g(x...
Let f & g be increasing and decreasing function respectively from [0, ∞) to [0, ∞). Let h(x) = f(g(x)) if h(0) = 0, h(x) – h(1) is
A
Always zero
B
Always negative
C
Always positive
D
Strictly increasing
Answer
Always zero
Explanation
Solution
Q f is increasing & g is decreasing \ h(x) fog(x) is
decreasing function
& h: [0, ) ® [0, ) & h(0) = 0
\ in [0, ) h(x) £ 0 but range of h(x) is [0, )
\ h(x) = 0
& h(x) – h(1) = 0 – 0 = 0