JEE Main20244 Apr 2024Evening ShiftMathematicsContinuity and DifferentiabilityActual

If the function f(x)= cases 72^x-9^x-8^x+1 2 - 1+ x , & x 0 a _e 2 _e 3 & , x=0 cases is continuous at x=0 , then the value of a^2 is equal to

Options

A968
B1152
C746
D1250

Correct answer

B. 1152

Step-by-step solution

aligned & _ x 0 f(x)=a 2 3 & _ n 0 72^x-9^x-8^x+1 2 - 1+ x = _ x 0 (8^x-1 ) (9^x-1 ) 2 - 1+ x & _ n 0 ( 8^x-1 x ) ( 9^x-1 x ) ( x^2 1- x )( 2 + 1+ x ) & 8 9 2 2 2 =24 2 2 3 & a=24 2 , a^2=576 2=1152 aligned

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