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Let A={x:-1 le x le 1}=B be a function f...

Let `A={x:-1 le x le 1}=B` be a function `f: A to B.` Then find the nature of each of the following functions.
(i) `f(x) = |x| " (ii) " f(x)=x|x|`
(iii) `f(x)=x^(3) " (iv) " f(x)="sin"(pi x)/(2)`

Text Solution

AI Generated Solution

To determine the nature of the functions given in the question, we will analyze each function step by step. ### Given: Let \( A = B = \{ x : -1 \leq x \leq 1 \} \) and we need to analyze the following functions: 1. \( f(x) = |x| \) 2. \( f(x) = x|x| \) 3. \( f(x) = x^3 \) ...
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