For the function fx-x2-19-x2x-1 - x- 19- x-1- which of the following statement is correct-

L.H.L.=lim_x→ 1^ (x+1)(x 1)(9 x^2)(x 1) =lim_x→ 1^ (x+1)(9 x^2)=16 R.H.L.=lim_x→ 1^+(x+1)(x 1)(9 x^2)(x 1) =lim_x→ 1^+(x+1)(9 x^2)=16 And f(1)=9 Here, clearly ...

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Byju's Answer

Standard XII

Mathematics

Right Hand Derivative

For the funct...

Question

For the function $f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} \frac{(x^{2} - 1) (9 - x^{2})}{x - 1}, & x \neq 1 9, & x = 1 \end{matrix}$ which of the following statement is correct?

f (x)

has missing point discontinuity.

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f (x)

has isolated point discontinuity.

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f (x)

has finite type discontinuity.

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f (x)

has infinite type discontinuity.

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Solution

The correct option is B $f (x)$ has isolated point discontinuity.
$L . H . L . = lim x \to 1^{-} \frac{(x + 1) (x - 1) (9 - x^{2})}{(x - 1)}$
$= lim x \to 1^{-} (x + 1) (9 - x^{2}) = 16$
$R . H . L . = lim x \to 1^{+} \frac{(x + 1) (x - 1) (9 - x^{2})}{(x - 1)}$
$= lim x \to 1^{+} (x + 1) (9 - x^{2}) = 16$

And $f (1) = 9$
Here, clearly limit exists but not equal to $f (1) .$
Hence, $f (x)$ has Isolated point discontinuity at $x = 1$ .

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For the function f(x)=⎧⎪⎨⎪⎩(x2−1)(9−x2)x−1,x≠19,x=1 which of the following statement is correct?

For the function $f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} \frac{(x^{2} - 1) (9 - x^{2})}{x - 1}, & x \neq 1 9, & x = 1 \end{matrix}$ which of the following statement is correct?