Question

Let $S$ be the set of all triangles and $R^{+}$ be the set of positive real numbers. Then the function $f:S\to R^{+},f\left(△\right)=\text{Area of}△,\text{where}△\in S$, is

• A. Injective but not surjective
• B. Surjective but not injective
• C. Injective as well as surjective
• D. Neither injective nor surjective

Answer 1

The correct option is B Surjective but not injective

For every positive real number $x$ there exist a triangle whose area is equal to $x.$

Hence the function $f:S\to R^{+}$ is surjective.

There could be two dissimilar triangles whose area is the same.

Hence, the function is not injective.