Solution Bank Exponential & Logarithmic Functions Target D
Answers to the Practice Problems are below in random order.
\(\begin{align}&\text{up 3}\ & \ \ \ &f^{-1}(x) = \ln\Big(-\frac{2x + 18}{5}\Big)+7\ & \ \ &\text{Dom:} (0, \infty),\ \text{Rng:} (-\infty, \infty),\ \text{VA:} x = 0\\\\
&11\ & \ \ \ &f^{-1}(x) =3^{\frac{x+2}{2}} + 11\ & \ \ &\text{reflecting in the x axis must be done before moving down 3}\\\\
&f^{-1}(x) =e^{3x + 9} - 1\ & \ \ \ &f^{-1}(x) = \ln(x) - 1\ & \ \ &\text{vertical stretch of 5, right 2, reflect in x axis}\\\\
&\text{left 3, down 6}\ & \ \ \ &f^{-1}(x) = 7^{\frac{x-2}{7}} + 4\ & \ \ &\text{Dom:}\ (0, \infty),\ \text{Rng:} (-\infty, \infty),\ \text{VA:} x = 0\\\\
&\text{vertical stretch of 3}\ & \ \ \ &f^{-1}(x) =\log_6\Big(\frac{x+11}{-2}\Big)-1\ & \ \ &\text{Dom:} (-9, \infty),\ \text{Rng:} (-\infty, \infty),\ \text{VA:} x = -9\\\\
&f^{-1}(x) =5^{2x-12}\ & \ \ \ &\text{vertical compression of}\ \frac{1}{2},\ \text{up 1}\ & \ \ &\text{Dom:} (0, \infty),\ \text{Rng:} (-\infty, \infty),\ \text{VA:} x = 0\\\\
&-\ln\;7\ & \ \ \ &f^{-1}(x) =\log_\frac{1}{2}\Big(\frac{x+6}{-4}\Big)-1\ & \ \ &\text{Dom:} (5, \infty),\ \text{Rng:} (-\infty, \infty),\ \text{VA:} x = 5\\\\
&\text{reflect in x axis, up 3}\ & \ \ &\text{right 2, reflect in x axis}\ & \ \ &\text{Dom:} (-1, \infty),\ \text{Rng:} (-\infty, \infty),\ \text{VA:} x = -1\end{align}\)
Answers to the Practice Problems are below in random order.
\(\begin{align}&\text{up 3}\ & \ \ \ &f^{-1}(x) = \ln\Big(-\frac{2x + 18}{5}\Big)+7\ & \ \ &\text{Dom:} (0, \infty),\ \text{Rng:} (-\infty, \infty),\ \text{VA:} x = 0\\\\
&11\ & \ \ \ &f^{-1}(x) =3^{\frac{x+2}{2}} + 11\ & \ \ &\text{reflecting in the x axis must be done before moving down 3}\\\\
&f^{-1}(x) =e^{3x + 9} - 1\ & \ \ \ &f^{-1}(x) = \ln(x) - 1\ & \ \ &\text{vertical stretch of 5, right 2, reflect in x axis}\\\\
&\text{left 3, down 6}\ & \ \ \ &f^{-1}(x) = 7^{\frac{x-2}{7}} + 4\ & \ \ &\text{Dom:}\ (0, \infty),\ \text{Rng:} (-\infty, \infty),\ \text{VA:} x = 0\\\\
&\text{vertical stretch of 3}\ & \ \ \ &f^{-1}(x) =\log_6\Big(\frac{x+11}{-2}\Big)-1\ & \ \ &\text{Dom:} (-9, \infty),\ \text{Rng:} (-\infty, \infty),\ \text{VA:} x = -9\\\\
&f^{-1}(x) =5^{2x-12}\ & \ \ \ &\text{vertical compression of}\ \frac{1}{2},\ \text{up 1}\ & \ \ &\text{Dom:} (0, \infty),\ \text{Rng:} (-\infty, \infty),\ \text{VA:} x = 0\\\\
&-\ln\;7\ & \ \ \ &f^{-1}(x) =\log_\frac{1}{2}\Big(\frac{x+6}{-4}\Big)-1\ & \ \ &\text{Dom:} (5, \infty),\ \text{Rng:} (-\infty, \infty),\ \text{VA:} x = 5\\\\
&\text{reflect in x axis, up 3}\ & \ \ &\text{right 2, reflect in x axis}\ & \ \ &\text{Dom:} (-1, \infty),\ \text{Rng:} (-\infty, \infty),\ \text{VA:} x = -1\end{align}\)