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The domain of definition of the functions $y (x)$ given by the equation $a^{x} + a^{y} = a (a > 1)$ is

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0≤x≤1

−∞

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detailed solution

Correct option is C

ax−1+ay−1=1⇒ay−1=1−ax−1⇒(y−1)log⁡a=log⁡1−ax−1R.H.S. is defined if 1−ax−1>0⇒ax−1<1=a∘⇒x−1<0 as a>1⇒ x<1 and the required domain is −∞

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The domain of definition of the functions y(x) given by the equation ax+ay=a(a>1) is

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The domain of definition of the functions $y (x)$ given by the equation $a^{x} + a^{y} = a (a > 1)$ is