Let f : A [ ] B be a function defined as f(x) = [x - 1 x - 2,] Where A = R - 2 and B = R -…

Question

Let  f : A $$ \to $$ B be a function defined as f(x) = $${{x - 1} \over {x - 2}},$$ Where A = R - {2} and B = R - {1}.  Then   f   is  :

Accepted Answer

Assume,

y = f(x)

$$ \Rightarrow $$ y = $${{x - 1} \over {x - 2}}$$

$$ \Rightarrow $$ yx - 2y = x - 1

$$ \Rightarrow $$ (y - 1)x = 2y - 1

$$ \Rightarrow $$ x = $${{2y - 1} \over {y - 1}}$$ = f -1(y)

As on the given domain the function is invertible and its inverse can be computed as shown above.

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