InterviewSolution
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InterviewSolution
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Which of the following functions has inverse function?`f: Zvecd efin e db yf(x)=x+2``f: Zvecd efin e db yf(x)=2x``f: Zvecd efin e db yf(x)=x``f: Zvecd efin e db yf(x)=|x|` |
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Answer» `f:Z to Z ,f(x) = x+2` is both one-one and onto. Hence invertible. `f:Z to Z ,f(x) = 2x` is one-one but not onto as range is set `{…,-4,-2,0,2,4,6, …}`. Hence not invertible. `f:Z to Z ,f(x) = x` is one-one and onto, Hence invertible. `f:Z to Z ,f(x) = |x|` is many-one, Also, range is `{0,1,2,3,...}`, So, into, Hence not invertible. |
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