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consider the function f:R rarr R,f(x)=(x...

consider the function `f:R rarr R,f(x)=(x^(2)-6x+4)/(x^(2)+2x+4)`
Range of fX() is

A

`((-oo,-(2)/(3))] cup[2,0)`

B

`[(-1)/(3),5]`

C

`(-oo,2)cup[(7)/(3),oo)`

D

`(20,oo)`

Text Solution

Verified by Experts

The correct Answer is:
2
`f(X)=(x^(2)-6x+4)/(x^(2)+2x+4)=1-(8x)/(x^(2)+2x+4)`
`f(x)-8((x^(2)+2x+4)-x(2x+2))/((x^(2)+2x+4)^(2)]`
`f(X)=0 rarrx2 or -2`
`f(2)=(4-12+4)/(4+4+4)=-4/12=-1/3`
`f(2)=(4+12+4)/(4-4+4)=5`
The graph of y =f(X) is as shown
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