The function fails to have an inverse when defined on because

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

The function

f(x)=x^{2}

fails to have an inverse when defined on

\mathbb{R}

because (a) its graph fails the vertical line test, so it is not a function. (b) it is not one–to–one; for example, the horizontal line

y=4

cuts its graph at two points. (c) its graph is not symmetric about the line

y=x

. (d) its range is not

\mathbb{R}

, therefore an inverse cannot be defined.