InterviewSolution
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InterviewSolution
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Which of the following functions is an odd functions ?A. `f(x)=sqrt(1+x+x^(2))-sqrt(1-x+x^(2))`B. `f(x)=x((a^(x)+1)/(a^(x)-1))`C. `f(x)=log_(10)((1-x^(2))/(1+x^(2)))`D. f(x)=k (constant ) |
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Answer» Correct Answer - A If ` f(x)=sqrt(1+x+x^(2))-sqrt(1-x+x^(2))`, then `f(-x)=sqrt(1-x+x^(2))-sqrt(1+x+x^(2))` `implies f(-x)=-f(x)` So, f (x) is an odd functions Thus, option (a) is correct . If `f(x)=x((a^(x)+1)/(a^(x)-1))`, then ` f(-x)=x((a^(-x)+1)/(a^(-x)-1))=-x((1+^(x))/(1-a^(x)))=x((a^(x)+1)/(a^(x)-1))-f(x)` So, f(x) is an even function. Thus , option (b) is not correct. If `f(x)=log_(10)((1-x^(2))/(1+x^(2)))`, then `f(-x)=log_(10)((1-x^(2))/(1+x^(2)))=f(x)` So, f(x) is an even function. Thus, option (c ) is not correct If f(x)=k for all `x ` then `f(-x)=f(x) ` for all `ximplies f(x)` is an even functions. |
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