Question

The function $f:R\to R$ given by $f\left(x\right)=x^3-1$ is

• A. A one-one function
• B. An onto function
• C. A bijection
• D. Neither one-one nor onto

Answer 1

Answer: (C)

A bijection

Given, $f\left(x\right)=x^3-1$
Let $x_1,x_2ϵR$
Now, $f\left(x_1\right)-f\left(x_2\right)$
$\Rightarrow x_1^3-1=x_2^3-1$
$\Rightarrow x_1^3=x_2^3$
$\Rightarrow x_1=x_2$
$\therefore f\left(x\right)$ is one-one. Also, it is onto as range of $f=R$.
Hence, it is a bijection.