Question

Statement 1: $f\left(x\right)={\log }_{e}x$ cannot be expressed as the sum of odd and even functions
Statement 2: $f\left(x\right)={\log }_{e}x$ is neither odd nor even function

• A. If both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1
• B. If both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT 1
• C. If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE
• D. If STATEMENT 1 is FALSE and STATEMENT 2 is TRUE

Answer 1

The correct option is B If both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT 1

Let $f\left(x\right)=\ln x$
Now the $\log$ input cannot be negative.
Hence if $x$ is a positive number
$f\left(x\right)=log\left(x\right)$
and $f(-x)$ does not exists. Hence the logarithmic function cannot be expressed as a sum of odd or even function since it itself is neither odd nor even in nature.