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If function f and g given by f (x)=log...

If function f and g given by
`f (x)=log(x-1)-log(x-2)and g(x)=log((x-1)/(x-2))"are equal"`
then x lies in the interval.

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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OBJECTIVE RD SHARMA-FUNCTIONS-Chapter Test
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  2. The number of bijective functions from set A to itself when A contains...

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  3. If f(x)=|sin x| then domain of f for the existence of inverse of

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  4. The functions f:[-1/2, 1/2] to [-pi/2, pi/2] defined by f(x)=sin^(-1)(...

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  5. Let f : R->R be a function defined by f(x)=(e^(|x|)-e^(-x))/(e^x+e^(...

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  6. If f: (e,oo) rarr R & f(x)=log[log (logx)], then f is -

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  7. Let f: R-{n}->R be a function defined by f(x)=(x-m)/(x-n) such that m!...

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  8. The inverse of the function f(x)=(e^x-e^(-x))/(e^x+e^(-x))+2 is given ...

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  9. Find the inverse of the function :y=(1 0^x-1 0^(-x))/(1 0^x+1 0^(-x))+...

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  10. Let f(x+(1)/(x))=x^(2)+(1)/(x^(2)),(x ne 0) then f(x) equals

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  11. Let f:R to R, g: R to R be two functions given by f(x)=2x-3,g(x)=x^(3)...

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  12. If g(x)=1+sqrtx and f(g(x))=3+2sqrtx+x then f(x) is equal to

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  13. If f(x)=(1-x)/(1+x), x ne 0, -1 and alpha=f(f(x))+f(f((1)/(x))), then

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  14. Let f:R to R be a function defined by f(x)=(x^(2)-8)/(x^(2)+2). Then f...

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  15. Let f:(-oo,2] to (-oo,4] be a function defined by f(x)=4x-x^(2). Then,...

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  16. The inverse of the function of f:R to R given by f(x)=log(a) (x+sqrt(x...

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  17. f:R to R is defined by f(x)==(e^(x^(2))-e^(-x^(2)))/(e^(x^(2))+e^(-x^(...

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  18. If f(x)=log((1+x)/(1-x)), "then f "((2x)/(1+x^(2))) is equal to

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  19. If f(x)=(2^x+2^(-x))/2 , then f(x+y)f(x-y) is equals to

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  20. The function f:R to R given by f(x)=x^(2)+x is

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  21. Let f:R to R and g:R to R be given by f(x)=3x^(2)+2 and g(x)=3x-1 for ...

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