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BITSAT 2017
Exam
BITSAT
Year
2017
Subject
Mathematics
Chapter
Functions

BITSAT 2017 · Mathematics · Functions

Let A = [-1, 1] and f: A → A be defined as f (x) = x |x| for all x...

Let A=[−1,1]andA = \left[-1, 1\right] andf: A \to Abedefinedasbe defined asf \left(x\right) = x \left|x\right|forallfor allx \in A,then, thenf\left(x\right)$ isLet A = [-1, 1] and f: A → A be defined as f (x) = x |x| for all x ∈ A , then f(x) is

Options

  1. Amany one and into function
  2. Bone-many and into function
  3. Cmany-one and into function
  4. Done-one and onto function

Correct answer

D. one-one and onto function

Step-by-step solution

f\left(x\right) = x\left|x\right| = \left\{{x2,x≥0−x2,x<0\begin{cases}x^{2}, & x \ge 0 \\ - x^{2}, & x < 0\end{cases}\right)

Let A = [-1, 1] and f: A → A be defined as f (x) = x |x| for all x ∈ A , then f(x) is

Since, −1≤x≤1- 1 \le x \le 1, therefore −1≤f(x)≤1- 1 \le f\left(x\right) \le 1

∴∴ Function is one-one and onto.

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