MonotonicityMedium
Question
If f and g are two increasing function such that fog is defined, then fog will be-
Options
A.increasing function
B.decreasing function
C.neither increasing nor decreasing
D.None of these
Solution
Let x1, x2 ∈ R such that x1 < x2
then
⇒ g(x1) < g(x2) {∵ g is an increasing function}
⇒ f(g(x1)) < f(g(x2)) (∵ f is an increasing function)
⇒ fog(x1) < fog(x2)
Hence, fog is an increasing function
then
⇒ g(x1) < g(x2) {∵ g is an increasing function}
⇒ f(g(x1)) < f(g(x2)) (∵ f is an increasing function)
⇒ fog(x1) < fog(x2)
Hence, fog is an increasing function
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