Ortega Olson
10/01/2023 · Junior High School
8 A function \( \mathrm{f}(x) \) is such that \( f(x)=\ln (2 x+3)+\ln 4 \), for \( x>a \), where \( a \) is a constant. (a) Write down the least possible value of \( a \). (b) Using your value of \( a \), write down the range of \( f \). (c) Using your value of \( a \), find \( \mathrm{f}^{-1}(x) \), stating its range.
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(a) The least possible value of \( a \) is \( -\frac{3}{2} \).
(b) The range of \( f \) is all real numbers greater than \( \ln 4 \).
(c) The inverse function \( f^{-1}(x) \) is \( f^{-1}(x) = \frac{e^{x} - 12}{8} \) with a range of \( \left(\ln 4, \infty\right) \).
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