Mathematics

Problem

Consider the function

f:\mathbb{R} \to \mathbb{R}

defined by

f(x)=3x-5

. a. (i) Solve the equation

f(x)=y

for a general

y \in \mathbb{R}

and hence show that

f

is surjective. b. (ii) If the codomain is changed to

(-\infty,\,2)

while the rule remains the same, determine whether the function is still surjective. Give reason for your answer.