Question

Let $f: R \rightarrow R$ be defined by $f(x) = 5^{|x|} + \text{sgn}(5^{-x})$, where sgn x denotes signum function of x. Then f is

• A. one-one but not onto
• B. onto but not one-one
• C. both one-one and onto
• D. neither one-one nor onto

Hint:

To test if a function is one-one, check if $f(x_1) = f(x_2)$ implies $x_1 = x_2$. A quick way is to find a counterexample, like $f(a) = f(-a)$ for functions involving $|x|$ or $x^2$. To test for onto, find the range of the function and compare it with the given co-domain.

Answer 1

The Correct Option is D