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Let S be the set of all triangles and $R^{+}$ be the set of positive real numbers. Then the function $f : S \to R^{+}, f (Δ) = a r e a o f Δ,$ where $Δ \in S$ is

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injective but not surjective

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injective as well as surjective

neither injective nor surjective

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detailed solution

Correct option is B

Two triangles may have equal areas∴ f is not one-one.Since each positive real number can represent area of triangle. ∴ f is onto.

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Let S be the set of all triangles and R+ be the set of positive real numbers. Then the function f:S→R+,f(Δ)=area of Δ, where Δ∈S is

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Let S be the set of all triangles and $R^{+}$ be the set of positive real numbers. Then the function $f : S \to R^{+}, f (Δ) = a r e a o f Δ,$ where $Δ \in S$ is