Question

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

• A. One-one and onto
• B. Many-one and onto
• C. One-one and into
• D. Many-one and into

Answer 1

Answer: (D)

$6^x>0$, $6^{|x|}>0$ for all $x\in R$.
So, $f$ is into. For different values of $x$, $6^x$ and $6^{|x|}$ are different positive numbers. Clearly, $f$ is many-one.