MHT CET20244 May 2024Evening ShiftMathematicsFunctionsActual

If f (x)= x 2-x , ~g (x)= x+1 x+2 , then (gogof) (x)=

Options

A6+x 10-2 x
B6-x 10+2 x
C6+x 10+2 x
D6-x 10-2 x

Correct answer

D. 6-x 10-2 x

Step-by-step solution

f(x)= x 2-x , g(x)= x+1 x+2 ( gof )(x)= x 2-x +1 x 2-x +2 aligned & (gogof) (x)= x 2-x +1 x +1 x 2-x +2 x 2-x +2 +2 & = x+2-x x+4-2 x +1 x+2-x x+4-2 x +2 aligned aligned & = 2 4-x +1 2 4-x +2 & = 2+4-x 2+8-2 x & = 6-x 10-2 x aligned

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