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Let A = [–1, 1]. discuss whether the following functions defined on A are one-one, onto or bijective: h(x) = x|x|

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one month ago Anand Kumar Pandey
1532 Points
```							Dear Studenth (x) = x|x|Let h (x1) = h (x2)x1|x1| = x2|x2|If x1,x2>0x1^2= x2^2x1^2–x2^2=0(x1–x2)(x1+x2)=0x1=x2(as x1+x2≠0)Similarly for x1, x2< 0, we have x1= x2It’s clearly seen thatfor x1and x2of opposite sign, x1≠x2.Hence, f (x) is one-one.For x ∈ [0,1]f(x) = x^2∈[0,1]For x<0,f(x) = – x^2  ∈[-1,0)Hence, the range is [-1, 1].Thus, h (x) is onto.Therefore, h (x) is bijectiveThanks
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one month ago
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