If f x - eft begin matrix ax - 2- b- - when 0 leq x -12 - -when x-1x-1- - when 1-x leq 2lend 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 above f(1) = 2 lim_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

Differentiabilty

If f x = eft ...

Question

If $f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} a x^{2} - b, & w h e n 0 \leq x < 1 2, & w h e n x = 1 x + 1, & w h e n 1 < x \leq 2 \end{matrix}$ 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
$f (1) = 2 {lim}_{x \to 1 -} f (x) = a - b {lim}_{x \to 1 +} f (x) = 2 \Rightarrow a - b = 2$
All the given sets of a, b make f(x) continuous at x =1.

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If $f (x) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} x^{2}, w h e n x < 0 x, w h e n 0 \leq x < 1 \frac{1}{x}, w h e n x > 1 \end{matrix}$
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If f(x)=⎧⎪⎨⎪⎩ax2−b,when0≤x<12,whenx=1x+1,when1<x≤2 is continuous at x = 1, then the most suitable value of a, b are

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

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

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