If f x - left begin matrix a x- 2-b- -when - 0 leq x-1 2- -when - x -1x-1- -when -x leq 2 lend matrix -right- is continuous at x-1- then the most suitable value of a- b areA- a-2- b-0B- a-1- b-1C- a -4- b -2D- All the above

The correct option is D All the abovelim_x → 1 f(x)=a b, lim_x → 1+f(x) 2 ⇒ a b=2 All the given sets of a, b make f(x) continuous at x=1. ...

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Byju's Answer

Standard XII

Mathematics

Inequality

If f x = left...

Question

If $f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} a x^{2} - b, & w h e n 0 \leq x < 1 2, & w h e n x = 1 x + 1, & w h e n < x \leq 2 \end{matrix}$ is continuous at x = 1, then the most suitable value of a, b are

a = 2, b = 0

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a = 1, b =-1

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a = 4, b = 2

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All the above

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Solution

The correct option is D All the above
${lim}_{x \to 1 -} f (x) = a - b, {lim}_{x \to 1 +} f (x) - 2 \Rightarrow a - b = 2$
All the given sets of a, b make f(x) continuous at x=1.

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If f(x)=⎧⎪⎨⎪⎩ax2−b,when 0≤x<12,when x=1x+1,when <x≤2 is continuous at x = 1, then the most suitable value of a, b are

The correct option is D All the abovelimx→1−f(x)=a−b, limx→1+f(x)−2⇒a−b=2 All the given sets of a, b make f(x) continuous at x=1.

If $f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} a x^{2} - b, & w h e n 0 \leq x < 1 2, & w h e n x = 1 x + 1, & w h e n < x \leq 2 \end{matrix}$ is continuous at x = 1, then the most suitable value of a, b are

The correct option is D All the above
${lim}_{x \to 1 -} f (x) = a - b, {lim}_{x \to 1 +} f (x) - 2 \Rightarrow a - b = 2$
All the given sets of a, b make f(x) continuous at x=1.