Find the inverse of each function.
1) \(g\left(x\right)=\frac{4}{3}x-6\)
2) \(z\left(x\right)=5+\sqrt{x}\)
3) \(w\left(x\right)=\large\frac{2x-3}{x+4}\)
4) \(u\left(x\right)=\large\frac{9x-2}{x+5}\)
Use the definition of inverse functions to verify that each pair of functions are or are not inverse functions.
5) \(f\left(x\right)=9x+4\) \(g\left(x\right)=\large\frac{1}{3}x\normalsize-2\)
6) \(f\left(x\right)=\large\frac{6}{5x-4}\) \(g\left(x\right)=\large\frac{6}{5x}+\frac{4}{5}\)
7) \(f(x)=\large\frac{7}{2x+3}\) \(g\left(x\right)\ =\ \large\frac{7}{2x}-\frac{3}{2}\)
8) Sketch a graph of the inverse of the function of \(y=\left(x+3\right)^2-1\).
1) \(g\left(x\right)=\frac{4}{3}x-6\)
2) \(z\left(x\right)=5+\sqrt{x}\)
3) \(w\left(x\right)=\large\frac{2x-3}{x+4}\)
4) \(u\left(x\right)=\large\frac{9x-2}{x+5}\)
Use the definition of inverse functions to verify that each pair of functions are or are not inverse functions.
5) \(f\left(x\right)=9x+4\) \(g\left(x\right)=\large\frac{1}{3}x\normalsize-2\)
6) \(f\left(x\right)=\large\frac{6}{5x-4}\) \(g\left(x\right)=\large\frac{6}{5x}+\frac{4}{5}\)
7) \(f(x)=\large\frac{7}{2x+3}\) \(g\left(x\right)\ =\ \large\frac{7}{2x}-\frac{3}{2}\)
8) Sketch a graph of the inverse of the function of \(y=\left(x+3\right)^2-1\).
9) Let \(f\) be a one to one function with domain \(A \) and range \( B \). Let \( g \) be a function with domain \( B \) and range \( C \). If \( y \in B \), then which of the following is true?
i) There is an \( x \in A \) such that \(f^{-1}(y)=x \)
ii) There is a \( z \in C \) such that \( g(y) = z \)
iii) \( y \) and \( z \) from above are the same element
iv) \( C \) is a subset of \( A \)
i) There is an \( x \in A \) such that \(f^{-1}(y)=x \)
ii) There is a \( z \in C \) such that \( g(y) = z \)
iii) \( y \) and \( z \) from above are the same element
iv) \( C \) is a subset of \( A \)