NIMCET 2025 Paper

Section: Mathematics

Question : 41 of 120

Marks: +1, -0

Let

g : R ⟶ R

and

h : R ⟶ R

be two functions such that

h(x)={\ sgn}(g(x)) .

(Here

R

is the set of all real numbers and sgn is the signum function.)
Which of the following is NOT true?

The domain of continuity of $h(x)$ equals the domain of continuity of $g(x)$ minus $\{x ∈ R : g(x)=0\}$
$g(x)$ is continuous at $g(x)=0$
The domain of $h(x)$ is the same as the domain of $g(x)$
The domain of $h(x)$ is different from the domain of $g(x)$ at the same point

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