MHT CET202123 Sep 2021Morning ShiftMathematicsContinuity and DifferentiabilityActual

If the function f(x)= cases 3 a x+b, & for x 1 cases x=1 . Then, the values of a and b are

Options

Aa=2, b=3
Ba=3, b=3
Ca=2, b=2
Da=3, b=2

Correct answer

D. a=3, b=2

Step-by-step solution

aligned & _ x 1⁻ f(x)= _ x 1⁻ 3 a x+b=3 a+b & _ x 1⁺ f(x) _ x 1⁺ 5 a x-2 b=5 a-2 b aligned f(1)=11 and function is continuous at x=1 , so we write 3 a + b =11=5 a -2 ~b 2 a =3 ~b This condition is satisfied when a =3, ~b =2

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