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If g(x)=x^2+x-2a n d1/2gof(x)=2x^2-5x+2,...

If `g(x)=x^2+x-2a n d1/2gof(x)=2x^2-5x+2,` then which is not a possible `f(x)?` `2x-3` (b) `-2x+2` `x-3` (d) None of these

A

`2x-3`

B

`2x+3`

C

`2x^(2)+3x+1`

D

`2x^(2)-3x-1`

Text Solution

Verified by Experts

The correct Answer is:
A
We have `(1)/(2)"g of "(x)=2x^(2)-5x+2`
`Rightarrow g(f(x))=4x^(2)-10x+4`
`(f(x))^(2)+f(x)-2=4x^(2)-10x+4`
`(f(x))^(2)+f(x)-(4x^(2)-10x+6)=0`
`f(x)=(-1pmsqrt(1+4(4x^(2)-10x+6)))/(2)`
`f(x)=(-1pmsqrt((16x^(2)-40x+25)))/(2)`
`f(x)=(-1pm(4x-5))/(2)=2x-3,-2x+2`
Hence, `f(x)=2x-3`
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OBJECTIVE RD SHARMA ENGLISH-FUNCTIONS-Chapter Test
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  14. Let f:R to R be a function defined by f(x)=(x^(2)-8)/(x^(2)+2). Then f...

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  15. If f:(-oo,2]to (-oo,4] where f(x), then f ^(-1) (x) is given by :

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  16. Find the inverse of the function, (assuming onto). " " ...

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  19. If f(x)=(2^x+2^(-x))/2 , then f(x+y)f(x-y) is equals to 1/2{f(2x)+f(2y...

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  20. The function f:R to R given by f(x)=x^(2)+x is

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