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The domain of definition of the function...

The domain of definition of the function `f(x)={x}^({x})+[x]^([x])` is where `{dot}` represents fractional part and `[dot]` represent greatest integral function). (a)`R-I` (b) `R-[0,1]` (c)`R-{Iuu(0,1)}` (d) `Iuu(0,1)`

A

`R-I`

B

`R-{0,1)`

C

`R-{I cup (0,1)}`

D

`I cup (0,1)`

Text Solution

Verified by Experts

The correct Answer is:
C
` f(x)={x}^({x})+[x]^([x])`
Here, base {x} and [x] should not be zero.
Hence, ` x notin I " and " x notin [0,1).`
Thus, domain is `R-{I cup (0,1)}.`
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