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Priyanka Subhash Pathak
Asked: 2022-11-10T11:37:50+05:30 In:

If `f(x) = log_(e^2x) ((2lnx+2)/(-x))` and `g(x) = {x}` then range of `g(x)` for existance of `f(g(x))` is
A. `(0, 2//e)`
B. `(0, 1//e) – {1//e^(2)}`
C. `(0, 3//e)`
D. none of these

If `f(x) = log_(e^2x) ((2lnx+2)/(-x))` and `g(x) = {x}` then range of `g(x)` for existance of `f(g(x))` is
A. `(0, 2//e)`
B. `(0, 1//e) – {1//e^(2)}`
C. `(0, 3//e)`
D. none of these
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  1. Correct Answer – B
    We have
    `f(x) log_(e^(2)x)((2 In x +2)/(-x)) and g(x) = {x}`
    For f(x) to real, we must have
    `x lt 0, x ne (1)/(e^(2)) and ((2 In (x) +2)/(-x)) gt 0`
    Now ,`((2 In x +2))/(-x) lt 0 and x gt 0`
    `rArr Inx + 2 lt 0 rArr In x lt-1 rArr x lte^(-k) rArr x lt(1)/(2)`
    Thus, f(x) is defined if
    `x in (0,1//e) – [1//e^(2)]`

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