Question

Let f(x) = |x - 2| + |x - 3| + |x - 4| and g(x) = f(x + 1). Then?

• A. g(x) is an even function
• B. g(x) is an odd function
• C. g(x) is neither even nor odd
• D. None of these

Answer 1

The correct option is C g(x) is neither even nor odd

g(x) = f(x + 1) = |x - 2 + 1| + |x - 3 + 1| + |x - 4 + 1| = |x - 1| + |x - 2| + |x - 3|.
Obviously, this is neither odd nor even.

Alternatively:
We know the graph of this function will neither be symmetrical to axis nor origin.