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Let f:R->[1,oo) be defined as f(x)=log10...

Let `f:R->[1,oo)` be defined as `f(x)=log_10(sqrt(3x^2-4x+k+1)+10)` If f(x) is surjective then k =

A

`k=(1)/(3)`

B

`klt(1)/(3)`

C

`kgt(1)/(3)`

D

`k=1`

Text Solution

Verified by Experts

The correct Answer is:
A
If f(x) is surjective then range of f(x) must be `[1,oo)`.
`therefore" Range of "sqrt(3x^(2)-4x+k+1)+10 in [0,oo)`
`rArr" Range of "3x^(2)-4x+k+1 in [0,oo)`
`rArr" "D=0`
`rArr" "16-12 (k+1)=0`
`rArr" "4-3k-3=0`
`rArr" "k=(1)/(3)`
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