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If f(x) =(2x+1)/(2x^3+3x^2+x) and S={x:f...

If `f(x) =(2x+1)/(2x^3+3x^2+x)` and `S={x:f(x)>0}` then S contains (a) `(-oo,-3/2)` (b) `(-3/2,-1/4)` (c)`(-1/4,1/2)` (d) `(1/2,3)`

Text Solution

Verified by Experts

`f(x) = (2x+1)/(2x^3+3x^2+x)`
`=>f(x) = (2x+1)/(x(2x^2+3x+1))`
`=>f(x) = (2x+1)/(x(x+1)(2x+1)) = 1/(x(x+1))`
As, `f(x) gt 0`, `:. 1/(x(x+1)) gt 0`
`=> x lt - 1 and x gt 0`
If we look at the options, option `(a)` and `(d)` satisfies the above condition. So, they are the correct option.
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