In each of the following cases,state whether the function is one-one,onto or bijective. Justify your answer. $f : R \rightarrow R$ defined by $f(x) = 3 - 4x$.

(D) Given $f : R \rightarrow R$ is defined by $f(x) = 3 - 4x$.
$1.$ Check for one-one:
Let $x_1, x_2 \in R$ such that $f(x_1) = f(x_2)$.
Then,$3 - 4x_1 = 3 - 4x_2$.
Subtracting $3$ from both sides,we get $-4x_1 = -4x_2$.
Dividing by $-4$,we get $x_1 = x_2$.
Since $f(x_1) = f(x_2) \implies x_1 = x_2$,the function $f$ is one-one.
$2.$ Check for onto:
Let $y \in R$ be any element in the codomain.
We want to find $x \in R$ such that $f(x) = y$.
$3 - 4x = y \implies 4x = 3 - y \implies x = \frac{3 - y}{4}$.
Since $y \in R$,$\frac{3 - y}{4}$ is also a real number $(R)$.
Thus,for every $y \in R$,there exists $x = \frac{3 - y}{4} \in R$ such that $f(x) = 3 - 4(\frac{3 - y}{4}) = 3 - (3 - y) = y$.
Since the range of $f$ is equal to the codomain $R$,the function $f$ is onto.
Conclusion:
Since the function is both one-one and onto,it is bijective.