JEE Main202523 Jan 2025Evening ShiftMathematicsFunctionsActual

Let the range of the function f(x)=6+16 x ( 3 -x ) ( 3 +x ) 3 x 6 x, x R be [ , ] . Then the distance of the point ( , ) from the line 3 x+4 y+12=0 is :

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Correct answer

A. 11

Step-by-step solution

aligned & f(x)=6+16 x ( 3 -x ) & ( 3 +x ) 3 x 6 x & f(x)=6+4 3 x 3 x 6 x & f(x)=6+ 12 x & Range of f(x)=[5,7] & [ , ]=[5,7] aligned Distance of point from 3 x+4 y+12=0 aligned & = | 3.5+4.7+12 3^2+4^2 | & =11 units aligned

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