Question

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

• A. a one-one function
• B. an onto function
• C. a bijection
• D. neither one-one nor onto

Answer 1

Answer: (C)

Given, $f(x)=x^3-1$
Let $x_1,x_2\in R.$
Now, $f(x_1)=f(x_2)$
$\Rightarrow$ $x_1^3-1=x_2^3-1$
$\Rightarrow$ $x_1^3=x_2^3\Rightarrow x_1=x_2$
$\therefore$ $f(x)$ is one-one. Also, it is onto. Hence, it is a bisection.