Mathematics - Functions Question with Solution | TestHub

MathematicsFunctionsDomain-RangeMedium2 minQB

MathematicsMediumsingle choice

If $e^{x} + e^{f (x)} = e$ , then for f(x)

Answer:

Solution:

$e^{f (x)} = e - e^{x} \Rightarrow f (x) = lo g_{e} (e - e^{x})$

$e - e^{x} > 0 \Rightarrow e^{1} > e^{x} \Rightarrow x < 1 D_{f} = (- \infty, 1)$

Let $y = f (x) = lo g_{e} (e - e^{x}) \Rightarrow e^{y} = e - e^{x}$

$\Rightarrow e^{x} = e - e^{y} \Rightarrow x = lo g_{e} (e - e^{y})$

$\Rightarrow e - e^{y} > 0 \Rightarrow e^{1} > e^{y}$

$∴ y < 1 R_{f} = (- \infty, 1)$

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Domain-Range

⏱ 2mℹ️ Source: QB

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