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Find the domain of the function : f(x)=s...

Find the domain of the function : `f(x)=sqrt(4^x+8^((2/3)(2x-2))-13-2^(2(x-1)))`

Text Solution

Verified by Experts

The correct Answer is:
`[2,oo)`
`4^(x)=8^((2)/(3)(x-2))-13-2^(2(x-1)) ge 0`
or `4^(x)+(4^(x))/(16)-(4^(x))/(4) ge 13`
or `4^(x) ge 4^(2)" or " x in [2,oo)`
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Knowledge Check

  • The domain of the function f(x)= sqrt(x^2 is :

    A
    `-inftyltxltinfty`
    B
    `0ltxltinfty`
    C
    R-{0}
    D
    `R^+cup{0}`

  • The domain of the function f(x)=root(6)(4^(x)+8^(2//3(x-2))-52-2^(2(x-1))) is

    A
    (0,1)
    B
    `[3, infty]`
    C
    [1,0)
    D
    None of these

  • The domain of the function f(x)=sqrt(x^(2)) is :

    A
    `-ooltxltoo`
    B
    `0ltxltoo`
    C
    `R-{0}`
    D
    `0lexltoo`

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