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Let f(x)a n dg(x) be two continuous func...

Let `f(x)a n dg(x)` be two continuous functions defined from `RvecR` , such that `f(x_1)` > `f(x_2)` and `g(x_1)` < `g(x_2)` `for all` `x_1`>`x_2` `dot` Then what is the solution set of `f(g(alpha^2-2alpha)` > `f(g(3alpha-4))`

Text Solution

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From the given information ,f is increasing and g is decreasing in R.
Now `f(g(alpha)^(2)-2alpha)gtf(g(3alpha-4))`
since f is increasing we, have
`g(a)^(2)-2(alpha)gt g(3alpha-4)`
`rarr(alpha)^(2)-5alpha+4lt0`
`rarr (alpha-1)(alpha-4)lt0`
`rarr` a in`(1,4)
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