Let $f: R→ R$ be defined as $f(x)=3x+4.$ Choose the correct answer.

f is injective and surjective f is many-one and onto f is injective and into f is neither injective nor surjective

f is injective and surjective

The correct answer is Option (1) → f is injective and surjective for $f(x_1)=f(x_2)$ $3x_1+4=3x_2+4$ $⇒x_1=x_2$ strictly ⇒ it is injective $y=3x+4⇒x=\frac{y-4}{3}$ so for any y in R atleast 1 value of x exist in R ⇒ it is surjective ⇒ f is injective and surjective