Let A = - 1 , 1 and f : A → A be defined as f x = x x for all x ∈ A , then f x is

f x = x x = x 2 , x ≥ 0 - x 2 , x < 0 Since, - 1 ≤ x ≤ 1 , therefore - 1 ≤ f x ≤ 1 ∴ Function is one-one and onto.

Mathematics - Functions Question with Solution | TestHub

MathematicsFunctionsTypes of Function (Mapping)Easy2 minPYQ_2017

MathematicsEasysingle choice

Let $A = [- 1, 1]$ and $f : A \to A$ be defined as $f (x) = x |x|$ for all $x \in A$ , then $f (x)$ is

Answer:

Solution:

$f (x) = x |x| = \{\begin{array}{cl} x^{2}, & x \geq 0 \\ - x^{2}, & x < 0 \end{array}$

Since, $- 1 \leq x \leq 1$ , therefore $- 1 \leq f (x) \leq 1$

$∴$ Function is one-one and onto.

Stream:BITSATSubject:MathematicsTopic:FunctionsSubtopic:Types of Function (Mapping)

⏱ 2mℹ️ Source: PYQ_2017

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