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The function f(x)=x2-25x+5 is continuous at x = -

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Question

The function `f(x) = (x^2 - 25)/(x + 5)` is continuous at x =

Options

  • – 5

  • x ∈ R

  • x ∈ R – |– 5|

  • None of these

MCQ

Solution

x ∈ R – |– 5|

Explanation:

At `x` = – 5, function f is not defined

∴ `f` is discontinuous at `x` = – 5

At `x = c ≠ - 5`

`lim_(x -> 0) f(x) = lim_(x -> 0) (x^2 - 25)/(x + 5)` = – 5

And `f(0)` = 0 – 5

 ∴ `f` is continous for all x ∈ R – |– 5|

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