First slide

Functions (XII)

Question

The function $f : R \to R$ defined by $f (x) = 4^{x} + 4^{| x |}$ is

Easy

A

One - one and into
B

Many - one and into
C

One - one and onto
D

Many - one and onto

Solution

$f (x) = \{\begin{cases} {2.4}^{x}, x \geq 0 \\ 4^{x} + 4^{- x}, x < 0 \end{cases}$
$4^{x} + 4^{- x} \geq 2 [A . M \geq G . M]$
From the graph

It is many-one and into.

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