Section 1
Inverse Functions
Determine whether each function is one-to-one. If it is one-to-one, find its inverse.$$f=\{(-4,3),(-2,-3),(2,-3),(6,13)\}$$
Determine whether each function is one-to-one. If it is one-to-one, find its inverse.$$g=\{(0,-7),(1,-6),(4,-5),(25,-2)\}$$
Determine whether each function is one-to-one. If it is one-to-one, find its inverse.$$h=\{(-5,-16),(-1,-4),(3,8)\}$$
Determine whether each function is one-to-one. If it is one-to-one, find its inverse.$$f=\{(-6,3),(-1,8),(4,3)\}$$
Determine whether each function is one-to-one. If it is one-to-one, find its inverse.$$g=\{(2,1),(5,2),(7,14),(10,19)\}$$
Determine whether each function is one-to-one. If it is one-to-one, find its inverse.$$h=\{(-1,4),(0,-2),(5,1),(9,4)\}$$
Determine whether each function is one-to-one.The table shows the average temperature during selected months in Tulsa, Oklahoma. The function matches each month with the average temperature, in 'F. Is it one-to-one?
Determine whether each function is one-to-one.The table shows some NCAA conferences and the number of schools in the conference. The function matches each conference with the number of schools it contains. Is it one-to-one?
Do all functions have inverses? Explain your answer.
What test can be used to determine whether the graph of a function has an inverse?
Determine whether each statement is true or false. If it is false, rewrite the statement so that it is true.$f^{-1}(x)$ is read as " $f$ to the negative one of $x$ "."
Determine whether each statement is true or false. If it is false, rewrite the statement so that it is true.If $f^{-1}$ is the inverse of $f$, then $\left(f^{-1} \circ f\right)(x)=x$ and $\left(f \circ f^{-1}\right)(x)=x$
Determine whether each statement is true or false. If it is false, rewrite the statement so that it is true.The domain of $f$ is the range of $f^{-1}$
Determine whether each statement is true or false. If it is false, rewrite the statement so that it is true.If $f$ is one-to-one and $(5,9)$ is on the graph of $f,$ then $(-5,-9)$ is on the graph of $f^{-1}$
Determine whether each statement is true or false. If it is false, rewrite the statement so that it is true.The graphs of $f(x)$ and $f^{-1}(x)$ are symmetric with respect to the $x$ -axis.
Determine whether each statement is true or false. If it is false, rewrite the statement so that it is true.Let $f(x)$ be one-to-one. If $f(7)=2,$ then $f^{-1}(2)=7$
For each function graphed here, answer the following.a) Determine whether it is one-to-one.b) If it is one-to-one, graph its inverse.
Find the inverse of each one-to-one function. Then, graph the function and its inverse on the same axes.$$g(x)=x-6$$
Find the inverse of each one-to-one function. Then, graph the function and its inverse on the same axes.$$h(x)=x+3$$
Find the inverse of each one-to-one function. Then, graph the function and its inverse on the same axes.$$f(x)=-2 x+5$$
Find the inverse of each one-to-one function. Then, graph the function and its inverse on the same axes.$$g(x)=4 x-9$$
Find the inverse of each one-to-one function. Then, graph the function and its inverse on the same axes.$$g(x)=\frac{1}{2} x$$
Find the inverse of each one-to-one function. Then, graph the function and its inverse on the same axes.$$h(x)=-\frac{1}{3} x$$
Find the inverse of each one-to-one function. Then, graph the function and its inverse on the same axes.$$f(x)=x^{3}$$
Find the inverse of each one-to-one function. Then, graph the function and its inverse on the same axes.$$g(x)=\sqrt[3]{x}+4$$
Find the inverse of each one-to-one function.$$f(x)=2 x-6$$
Find the inverse of each one-to-one function.$$g(x)=-4 x+8$$
Find the inverse of each one-to-one function.$$h(x)=-\frac{3}{2} x+4$$
Find the inverse of each one-to-one function.$$f(x)=\frac{2}{5} x+1$$
Find the inverse of each one-to-one function.$$g(x)=\sqrt[3]{x+2}$$
Find the inverse of each one-to-one function.$$h(x)=\sqrt[3]{x-7}$$
Find the inverse of each one-to-one function.$$f(x)=\sqrt{x}, x \geq 0$$
Find the inverse of each one-to-one function.$$g(x)=\sqrt{x+3}, x \geq-3$$
Given the one-to-one function $f(x)$, find the function values without finding the equation of $f^{-1}(x) .$ Find the value in a) before b).$f(x)=5 x-2$a) $f(1)$b) $f^{-1}(3)$
Given the one-to-one function $f(x)$, find the function values without finding the equation of $f^{-1}(x) .$ Find the value in a) before b).$f(x)=3 x+7$a) $f(-4)$b) $f^{-1}(-5)$
Given the one-to-one function $f(x)$, find the function values without finding the equation of $f^{-1}(x) .$ Find the value in a) before b).$f(x)=-\frac{1}{3} x+5$a) $f(9)$b) $\quad f^{-1}(2)$
Given the one-to-one function $f(x)$, find the function values without finding the equation of $f^{-1}(x) .$ Find the value in a) before b).$f(x)=\frac{1}{2} x-1$a) $f(6)$b) $f^{-1}(2)$
Given the one-to-one function $f(x)$, find the function values without finding the equation of $f^{-1}(x) .$ Find the value in a) before b).$f(x)=-x+3$a) $f(-7)$b) $f^{-1}(10)$
Given the one-to-one function $f(x)$, find the function values without finding the equation of $f^{-1}(x) .$ Find the value in a) before b).$f(x)=-\frac{5}{4} x+2$a) $f(8)$b) $f^{-1}(-8)$
Given the one-to-one function $f(x)$, find the function values without finding the equation of $f^{-1}(x) .$ Find the value in a) before b).$f(x)=2^{x}$a) $f(3)$b) $f^{-1}(8)$
Given the one-to-one function $f(x)$, find the function values without finding the equation of $f^{-1}(x) .$ Find the value in a) before b).$f(x)=3^{x}$a) $f(-2)$b) $f^{-1}\left(\frac{1}{9}\right)$
If $f(x)=x+9,$ show that $f^{-1}(x)=x-9$
If $f(x)=x-12,$ show that $f^{-1}(x)=x+12$
If $f(x)=-6 x+4,$ show that $f^{-1}(x)=-\frac{1}{6} x+\frac{2}{3}$
If $f(x)=-\frac{1}{7} x+\frac{2}{7},$ show that $f^{-1}(x)=-7 x+2$
If $f(x)=\frac{3}{2} x-9,$ show that $f^{-1}(x)=\frac{2}{3} x+6$
If $f(x)=-\frac{5}{8} x+10,$ show that $f^{-1}(x)=-\frac{8}{5} x+16$
If $f(x)=\sqrt[3]{x-10},$ show that $f^{-1}(x)=x^{3}+10$
If $f(x)=x^{3}-1,$ show that $f^{-1}(x)=\sqrt[3]{x+1}$