Let and be functions defined by and

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

5. Let

\mathrm{A}=\{-1,0,1,2\}, \mathrm{B}=\{-4,-2,0,2\}

and

f, g: \mathrm{A} \rightarrow \mathrm{B}

be functions defined by

f(x)=x^{2}-x, x \in \mathrm{~A}

and

g(x)=2\left|x-\frac{1}{2}\right|-1, x \in \mathrm{~A}

. Are

f

and

g

equal? Justify your answer. (Hint: One may note that two functions

f: \mathrm{A} \rightarrow \mathrm{B}

and

g: \mathrm{A} \rightarrow \mathrm{B}

such that

f(a)=g(a) \forall a \in \mathrm{~A}

, are called equal functions).