NIMCET 2018 — Mathematics PYQ

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Question

NIMCET 2018 — Mathematics PYQ

NIMCET | Mathematics | 2018

$f (x) = x + ∣ x ∣$ is continuous for

Choose the correct answer:

Explanation

Concept:
If $f (x) = f_{1} (x) + f_{2} (x)$ and
$f_{1} (x)$ and $f_{2} (x)$ are continuous function then $f (x)$ is continuous function.

Calculations:
Given function is $f (x) = x + ∣ x ∣$
$\Rightarrow f (x) = f_{1} (x) + f_{2} (x)$ where $f_{1} (x) = x$ and $f_{2} (x) = ∣ x ∣$
Here, $f_{1} (x) = x$ is continuous function at $x \in (- \infty, \infty)$
$f_{2} (x) = ∣ x ∣$ is continuous function at $x \in (- \infty, \infty)$
$\Rightarrow f (x)$ is continuous function at $x \in (- \infty, \infty)$
Hence, $f (x) = x + ∣ x ∣$ is continuous for $x \in (- \infty, \infty)$