Question

The function $f:R\to R$ defined by $f\left(x\right)=6^x+6^{|x|}$ is

• A. one one and onto
• B. many one and onto
• C. one one and into
• D. many one and into

Answer 1

The correct option is C one one and into

For $x>0$

$f\left(x\right)={2.6}^x$

For $x<0$

$f\left(x\right)=6^x+6^{-x}$

and $f\left(0\right)=2$

Hence, $f\left(x_1\right)=f\left(x_2\right)$

Implies $x_1=x_2$ and $f\left(x\right)$ will never give negative values,

Therefore, not an onto function

Hence, it is a one one function and into function.