Check the injectivity and surjectivity of the given functions: *f*: **R** → **R** given by *f*(*x*) = *x*^{2}

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#### Solution

*f*: **R** → **R** is given by,

*f*(*x*) = *x*^{2}

It is seen that *f*(−1) = *f*(1) = 1, but −1 ≠ 1.

∴ *f *is not injective.

Now,−2 ∈ **R**. But, there does not exist any element *x *∈ **R** such that *f*(*x*) = *x*^{2} = −2.

∴ *f* is not surjective.

Hence, function *f* is neither injective nor surjective.

Concept: Types of Functions

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