First slide

Functions (XII)

Question

The function f : R → R defined by, f (x) = 4^x + 4^|x| is

Moderate

A

one-one and into
B

many-one and into
C

one-one and onto
D

many-one and onto

Solution

Since, for different x, 4x and 4| x | are different positive numbers,
$∴$ f is one–one. Also, f is not onto as its range (0, ∞) is a proper subset of its co-domain R.

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