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# If $f:R\rightarrow R$ is defined as $f(x)=6^x+6^{|x|}$ then what type of function is $f$ ?

$\begin{array}{1 1} \text{1-1 not onto} \\ \text{onto but not 1-1} \\ \text{both 1-1 and onto} \\ \text{neither 1-1 nor onto} \end{array}$

Can you answer this question?

## 1 Answer

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• $|x|=x,$ if $x\geq 0$ and $|x|=-x,$ if $x$<0.
$f(x)=6^x+6^{|x|}$ $=2.6^x,$ if $x\geq0$
$f(x)=6^x+\large\frac{1}{6^x}$ if $x$<0
$=\large\frac{(6^x)^2+1}{6^x}$
Both $2\times 6^x\:\:and\:\:\large\frac{(6^x)^2+1}{6^x}$ are positive and not equal to 0.
$\therefore f$ is 1-1 and not onto
answered May 25, 2013

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