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Find the domain and range of each of the following real valuedfunction: `f(x)=(a x-b)/(c x-d)`. |
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Answer» Correct Answer - dom `(f)=R-{(d)/(c)}," range "(f)=R-{(a)/(c)}` `f(x)=(ax-b)/(cx-d)` si not defined when `cx-d=0impliesx=(d)/(c)` `:."dom "(f)=R-{(d)/(c)}`. Let y=f(x). Then, `y=(ax-b)/(cx-b)impliescxy-dy=ax-bimpliescxy=ax=dy-b` `impliesx(cy-a)=dy-bimpliesx=(dy-b)/(cy-a)`. Clearly, x is not defined when `cy-a=0impliesy=(a)/(c)`. `:."dom "(f)=R-{(a)/(c)}`. |
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