1is the option 3 correct?
if f:[1,10]→[1,10] is a non decreasing function and g:[1,10]→[1,10] is a non increasing function. let h(x)=f(g(x)) with h(1)=1
the h(2)
options
1) lies in (1,2)
2)is more than 2
3)is = to 1
4)is not defined
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5 Answers
1f'(x)≥0 for x≡[1,10]
g'(x)≤0 for x≡[1,10]
h(x)=fog(x)
therefore h'(x)=f'g(x)*g'(x) by chain rule
h'(x)≤0 because f'g(x)≥0 and g'(x)≤0
thus h(x) is either a decreasing or a constant function
thus h(2)≤h(1) for 2>1
thus h(2)≤1
only one option satisfies the above
notice that last option is incorrect as it comes in the domain of fog(x)
h(2) is defined
1@kaustab.....
g is non increasing...so either it can be constant or monotonical decreasing in its domain of definition.....
f(g(x))..with increase in x-->g(x) will decrease..
similarly f(x) is monotonical increasing function...
or constant...
if x-->decreasing f(x)-->decrease
so with x increasing f(g(x))-->is decreasing
h(1)=1
h(1)=f(g(1))=1
g(1)=max 10
f(10)=1
f=constant as it cant decrease further
so f(anything)=1
h=f(g(anything))=f(something)=1