Let A = [–1, 1] and f : A → A be defined as f (x) = x | x

1.	Let A = [–1, 1] and f : A → A be defined as f (x) = x \| x \| for all x ∈ A, then f (x) is(a) many-one into function (b) one-one into function (c) many-one onto function(d) one-one onto function.
Answer» Answer : (d) one-one onto function \(\ f(x) =x\|x\| =\begin{cases}x^2, &\quad x \geq 0\\-x^2, &\quad x<0\end{cases}\) Since – 1 ≤ x ≤ 1, therefore – 1 ≤ f (x) ≤ 1 ⇒ function is one-one onto.

Let A = [–1, 1] and f : A → A be defined as f (x) = x | x | for all x ∈ A, then f (x) is(a) many-one into function (b) one-one into function (c) many-one onto function(d) one-one onto function.

Answer»

Answer : (d) one-one onto function

\(\ f(x) =x|x| =\begin{cases}x^2, &\quad x \geq 0\\-x^2, &\quad x<0\end{cases}\)

Since – 1 ≤ x ≤ 1, therefore – 1 ≤ f (x) ≤ 1

⇒ function is one-one onto.