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Let `agt1` be a real number and `f(x)=log_(a)x^(2)" for "xgt 0.` If `f^(-1)` is the inverse function fo f and b and c are real numbers then `f^(-1)(b+c)` is equal toA. `f^(-1)(b).f^(-1)(c)`B. `f^(-1)(b)+f^(-1)(c)`C. `(1)/(f(b+c))`D. `(1)/(f^(-1)(b)+f^(-1)(c))` |
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Answer» Correct Answer - A `y=2log_(a^(x))` `rArr" "log_(a)x=(y)/(2)` `rArr" "x=a^(y//2)` `rArr" "f^(-1)(y)=a^(y//2)` `rArr" "f^(-1)(b+c)=a^((b+c)/(2))=a^((b)/(2)).a^((c)/(2))=f^(-1)(b).f^(-1)(c)` |
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