Question

The function f:R→R defined as f(x)=7x+4 is both one-one and onto.

(a) True

(b) False

I have been asked this question during an online interview.

I want to ask this question from Types of Functions in portion Relations and Functions of Mathematics – Class 12

Answer 1

The correct option is (a) True

The best explanation: The given statement is true. f is both one-one and onto.

For one-one: Consider f(x1)=f(x2)

∴7x1+4=7x2+4

⇒ x1=x2.

Thus, f is one – one.

For onto: Now for any real number y which lies in the co- domain R, there exists an element x=(y-4)/7

such that \(f(\frac{y-4}{7}) = 7*(\frac{y-4}{7}) + 4 = y\). Therefore, the function is onto.