InterviewSolution
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InterviewSolution
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Which of the following functions is one-one?A. `fR to R " is given by"f(x)=2x^(1)+1"For all " x in R`B. `g:Z to Z " given by"g(x)=x^(4)"For all " x in Z`C. `h:R to R " given h"(x)=x^(3)+4"For all " x in R`D. `phi:C to C " given by "phi(z)=z^(3)+4"For all " z in C` |
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Answer» Correct Answer - C We observe that f(1)=3 and f(-1)=3 `therefore 1 ne -1 " but "f(1)=f(-1)` So, f is not a one-one function. Clearly, `1,-1 in Z " such that "g(1)=1 and g(-1) =(-1)^(4)=1` `therefore 1 ne -1" but "g(1)=g(-1)` So, g is not a one-one fourth Let `x, y in R` be such that `h(x)=h(y) Rightarrow x^(3)+4=y^(3)+4 Rightarrow x^(3)=y^(3) Rightarrow x=y` `therefore h: R to R ` is one-one functions. We observe that `w, w^(2) in C` (w is a cube root of unity) such that `w ne w^(2)" but " phi(w)=w^(3)+4=5 and phi(w^(2))=w^(6)+4=5` `i.e. w ne w^(2)" but "ph(w)=phi(w^(2))` So, `phi` is not a one-one functions. |
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