A) \[{{f}^{-1}}(\alpha )-{{f}^{-1}}(\beta )\]
B) \[\frac{{{f}^{-1}}(\alpha )}{{{f}^{-1}}(\beta )}\]
C) \[\frac{1}{f(\alpha -\beta )}\]
D) \[\frac{1}{f(\alpha )-f(\beta )}\]
Correct Answer: B
Solution :
[b] \[f(x)=5lo{{g}_{5}}x\Rightarrow {{f}^{-1}}(x)={{5}^{x/5}}\] \[{{f}^{-1}}(\alpha -\beta )={{5}^{\frac{\alpha -\beta }{5}}}=\frac{{{5}^{\alpha /5}}}{{{5}^{\beta /5}}}=\frac{{{f}^{-1}}(\alpha )}{{{f}^{-1}}(\beta )}\]
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