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  • Let f: {R-3/5} → R be defined by f(x) = (3x + 2)/(5x - 3) then (a) f(x) = f(x)

Let f: \{ R-3/5 \} \rightarrow R be defined by f(x) = (3x + 2)/(5x - 3) then 

\\(a) f(x) = f(x); \\(b) f\textsuperscript{-1}(x) = - f(x) \\(c) (fof)x = - x \\(d) f\textsuperscript{-1}(x) = f(x)/19\\

Answers (1)

(a) 

Here,f(x) = (3x + 2)/(5x - 3) \forall x \neq 3/5\\

\\So, y = (3x + 2)/(5x - 3)\\ or, y (5x-3) = (3x + 2)\\ or, 5xy-3y = 3x + 2\\ or, x = (3y+2)/(5y-3)\\ Therefore, f\textsuperscript{-1}(x) = (3x+2)/(5x-3)\\ Hence, f\textsuperscript{-1}(x) = f(x)\\

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