Find the domain and the range of the function, `f(x)=(x^(2)-25)/(x-5)` – InterviewSolution

InterviewSolution

1.	Find the domain and the range of the function, `f(x)=(x^(2)-25)/(x-5)`.
Answer» We have, `f(x)=(x^(2)-25)/(x-5)` Clearly, f(x) is defined for all real values of x for which `x-5ne0,i.e.,xne5`. `:."dom "(f)=R-{5}`. Let y=f(x). Then, `y=(x^(2)-25)/(x-5)impliesy=x+5,"when "x-5ne0` `impliesy=x+5,"when "xne5` `impliesyne5+5impliesyne10`. Then, y can be assigned any real value except 10. `:."range "(f)=R-{10}`. Hence, dom `(f)=R-{5}"and range "(f)=R-{10}`.

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