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

The correct answer is Option (1) → f is injective and surjective

Injective (one-one): suppose \(f(x_1) = f(x_2)\).

    \(3x_1 + 4 = 3x_2 + 4\)
    \(x_1 = x_2\)

So different inputs give different outputs.

Surjective (onto): take any real number y. Solving 3x + 4 = y:

    \( \displaystyle x = \frac{y-4}{3} \)

This x is a real number and f(x) = y, so every real number is an output.

Hence f is both injective and surjective.