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If fogoh(x) is an increasing function, t...

If `fogoh(x)` is an increasing function, then which of the following is not possible? `f(x),g(x),a n dh(x)` are increasing `f(x)a n dg(x)` are decreasing and `h(x)` is increasing `f(x),g(x),a n dh(x)` are decreasing

Text Solution

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(i) f(x),g(x) and h(x) are increasing
`therefore x_(2) gt x_(1)` then `h(x_(2))geh(x_(1))`
g(x) is increasing
`therefore g(h(x_(2))geg(h(x_(1)))`
Also f(x) is increasing
`therefore` f(g(h(x))) is increasing
(ii) f(x) and g(x) are decreasing and h(x) is increasing h(x) is increasing
`therefore x_(2)gtx_(1)` then `h(x_(2))geh(x_(1))`
g(x) is decreasing , then
`g(h(x_(2)) leg(h(x_(1))`
Thus f(g(h(x)) is increasing
(iii) obviously when f(x),g(x) are h(x) are decreasing then f(g(h(x))is decreasing
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