Consider the function defined for all real

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Consider the function

g(x)=|x-4|

defined for all real

x

. Which of the following is TRUE about

g

? (a)

g

is onto

\mathbb R

because for every real

y

there exists

x

with

g(x)=y

(b) The range of

g

does not contain

0

, so

g

is not onto

\mathbb R

(c)

g

is not one-to-one because

g(3)=g(5)

(d)

g

is one-to-one because the absolute value makes all outputs unique