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Find for what values of x the following ...

Find for what values of `x` the following functions would be identical.
`f(x)=log(x-1)-log(x-2)` and `g(x)=log((x-1)/(x-2))`

A

[1,2]

B

`[2,oo]`

C

`[2,oo]`

D

`[-oo, oo]`

Text Solution

Verified by Experts

The correct Answer is:
C
f(x) is defined for all x satisfying
`x-1 gt 0 and x-2 gt 0 i.e. xgt 2`
`therefore "Domain (f)"=(2,oo)......(i)`
g (x) is defined for all x satisfying
`(x-1)/(x-2) gt 0 Rightarrow x in (-oo, 1) uu(2,oo)`
`therefore "Domain (g)"=(-oo,1) uu (2,oo).....(ii)`
Thus, f(x) and g(x) are equal for all x belonging to their common domain i.e. `(2,oo)`
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