Question

If S be the set of all triangles and $f:S\to R+,f\left(\Delta \right)$ =Area of $\Delta$, then $f$ is.

• A. one-one onto
• B. one-one into
• C. many-one onto
• D. many-one into

Answer 1

The correct option is C many-one onto

There can be infinitely many triangles with the same area.
Hence the above function is many one.
Now for every element $\left(△\right)$ in $R^{+}$ there is atleast one triangle in S which has $Area=△$.
Hence for every element in $R^{+}$ there is atleast one corresponding element in $S$ .
Hence $f\left(x\right)$ is an onto function.