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Solution for Function F(X) = Ax Is Increasing On R, If (A) A > 0 (B) A < 0 (C) 0 < A < 1 (D) A > 1 - CBSE (Science) Class 12 - Mathematics

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Question

Function f(x) = ax is increasing on R, if
(a) a > 0
(b) a < 0
(c) 0 < a < 1
(d) a > 1

Solution

(d) a > 1

\[f\left( x \right) = a^x \]

\[f'\left( x \right) = a^x \log a\]

\[\text { Given: f(x) is increasing on R .} \]

\[ \Rightarrow f'\left( x \right) > 0\]

\[ \Rightarrow a^x \log a > 0\]

\[ \Rightarrow a^x > 0 \left( \text { Logarithmic function is defined for positive values of a } \right)\]

\[\text { We know,} \]

\[ a^x \log a > 0\]

\[\text { It can be possible when} a^x > 0 \text { and } \log a > 0 or a^x < 0 and \log a < 0 \left( \text { Not possible, logarithmic function is defined for positive values of a } \right)\]

\[ \Rightarrow \log a > 0\]

\[ \Rightarrow a > 1\]

\[\text { So,f (x) is increasing when }a> 1 .\]

  Is there an error in this question or solution?
Solution Function F(X) = Ax Is Increasing On R, If (A) A > 0 (B) A < 0 (C) 0 < A < 1 (D) A > 1 Concept: Increasing and Decreasing Functions.
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