Question

Let $f:R\to R$ be defined by $f\left(x\right)=\left[x\right]$ and $g\left(x\right)=\frac{3-2x}{4}$. We can say:

• A. $f$ is neither one-one nor onto
• B. $g$ is one-one but $f$ is not one-one
• C. $f$ is one-one and $g$ is onto
• D. neither $f$ nor $g$ is onto

Answer 1

Answer: (A), (B)

$f$ is neither one-one nor onto
$g$ is one-one but $f$ is not one-one

$f\left(x\right)=1$ for $x=1.1$ and $x=1.2$ both. Hence f is not one-to-one.

Also range of f is the set Z. Hence f is not onto either.

Now g is a polynomial function, hence it must be bijective.

So option A and B are true.