Consider the function defined by

MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Consider the function

f:\mathbb R\to\mathbb R

defined by

f(x)=5x+7

. Answer the following. (i) Solve the equation

f(x)=y

for

x

in terms of

y

. (ii) Using the result of part (i), show that

f

is onto when its codomain is

\mathbb R

. (iii) Suppose the codomain is changed to the set

2\mathbb Z

of even integers. Determine whether

f: \mathbb R \to 2\mathbb Z

remains onto. Give a brief proof to support your conclusion.