Maths · The composition of functions
Assertion Let and be increasing and decreasing functions respectively from \) to
Assertion Let \( f \) and \( g \) be increasing and decreasing functions respectively from \( [0, \infty] \) to \( [0, \infty] . \operatorname{Let} h(x)=f(g(x)) . \) If \( h(0)=0, \) then \( h(x) \) is always zero Reason \( h(x) \) is an increasing function of \( x \)
- A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
- B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
- C. Assertion is correct but Reason is incorrect
- D. Both Assertion and Reason are incorrect
Step-by-step solution
Since f is increasing and g is decreasing, h(x) = f(g(x)) is decreasing (composition of decreasing with increasing yields decreasing). Given h(0)=0 and h(x) ≥ 0, we have h(x)=0 for all x, so Assertion is true. Reason claims h is increasing, which is false. Therefore, Assertion true, Reason false.
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