Question

Which of the following functions are one-one?

• A. $f:R\to R$ given by $f\left(x\right)={2x}^2+1$ for all $x\in R$
• B. $g:Z\to Z$ given by $g\left(x\right)=x^4$ for all $x\in R$
• C. $h:R\to R$ given by $h\left(x\right)=x^3+4$ for all $x\in R$
• D. $\varphi :C\to C$ given $\varphi \left(z\right)={2z}^6+4$ for all $x\in R$

Answer 1

The correct option is C $h:R\to R$ given by $h\left(x\right)=x^3+4$ for all $x\in R$

For all even powered function,
$f\left(x_1\right)=f\left(x_2\right)$ where $x_1=\pm \left(x_2\right)$
Hence, the only possible one-one function is $f\left(x\right)=x^3+4$
$f\left(x\right)$ is a strictly increasing function. So, it is one-one.