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Let f(x)=(20)/(4x^2-9x^2+6x) Statement...

Let `f(x)=(20)/(4x^2-9x^2+6x)`
Statement -1 : Range of f=[6,20]
Statement -2 f(x) increases (1/2,1) and decrease on `(1,oo) cup (-oo,0)cup (0,1//2)`

A

Statement-1 True statement -1 is True,Statement -2 is True statement -2 is a correct explanation for Statement-6

B

Statement-1 True statement -1 is True,Statement -2 is True statement -2 is not a correct explanation for Statement-6

C

Statement-1 True statement -1 is True,Statement -2 is False

D

Statement-1 is False ,Statement -2 is True

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x)=(20)/(x{(2x-9/4)^2+15/16})`
`rArr underset(x rarr0^-)limf(x)=-oo and , underset(x rarr0^+)limf(x)-oo`
Also , f(x) is contimuous on R-{0}
So range of f(x)`={-oo,oo}`
Hence ,statement-1 is not true
Again
`f(x)(20)/(4x^3-9x^3+6x)`
`rArr f(x)=(-20(12x^2-18x+6))/(4x^3-9x^2+6x)^2=(-120(2x-1)(x-1))/(4x^2-9x^2+6x)^2`
The signs of f' (x) for different values of x are as shown below: So f(x) is decreasing on `(-oo,0) cup (0,1//2) cup (1,oo)` and increasing in (1/2,1)
Hence ,statement-2 is true.
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