Section 1
Finding Composite and Inverse Functions
In the following exercises, find (a) $(f \circ g)(x),(b)(g \circ f)(x)$, and $(c)(f \cdot g)(x)$.$f(x)=4 x+3$ and $g(x)=2 x+5$
In the following exercises, find (a) $(f \circ g)(x),(b)(g \circ f)(x)$, and $(c)(f \cdot g)(x)$.$f(x)=3 x-1$ and $g(x)=5 x-3$
In the following exercises, find (a) $(f \circ g)(x),(b)(g \circ f)(x)$, and $(c)(f \cdot g)(x)$.$f(x)=6 x-5$ and $g(x)=4 x+1$
In the following exercises, find (a) $(f \circ g)(x),(b)(g \circ f)(x)$, and $(c)(f \cdot g)(x)$.$f(x)=2 x+7$ and $g(x)=3 x-4$
In the following exercises, find (a) $(f \circ g)(x),(b)(g \circ f)(x)$, and $(c)(f \cdot g)(x)$.$f(x)=3 x$ and $g(x)=2 x^2-3 x$
In the following exercises, find (a) $(f \circ g)(x),(b)(g \circ f)(x)$, and $(c)(f \cdot g)(x)$.$f(x)=2 x$ and $g(x)=3 x^2-1$
In the following exercises, find (a) $(f \circ g)(x),(b)(g \circ f)(x)$, and $(c)(f \cdot g)(x)$.$f(x)=2 x-1$ and $g(x)=x^2+2$
In the following exercises, find (a) $(f \circ g)(x),(b)(g \circ f)(x)$, and $(c)(f \cdot g)(x)$.$f(x)=4 x+3$ and $g(x)=x^2-4$
In the following exercises, find the values described.For functions $f(x)=2 x^2+3$ and $g(x)=5 x-1$, find(a) $(f \circ g)(-2)$(b) $(g \circ f)(-3)$(c) $(f \circ f)(-1)$
In the following exercises, find the values described.For functions $f(x)=5 x^2-1$ and $g(x)=4 x-1$, find(a) $(f \circ g)(1)$(b) $(g \circ f)(-1)$(c) $(f \circ f)(2)$
In the following exercises, find the values described.For functions $f(x)=2 x^3$ and $g(x)=3 x^2+2$, find(a) $(f \circ g)(-1)$(b) $(g \circ f)(1)$(c) $(g \circ g)(1)$
In the following exercises, find the values described.For functions $f(x)=3 x^3+1$ and $g(x)=2 x^2-3$, find(a) $(f \circ g)(-2)$(b) $(g \circ f)(-1)$(c) $(g \circ g)(1)$
In the following exercises, determine if the set of ordered pairs represents a function and if so, is the function one-to-one.$\{(-3,9),(-2,4),(-1,1),(0,0)$. $(1,1),(2,4),(3,9)\}$
In the following exercises, determine if the set of ordered pairs represents a function and if so, is the function one-to-one.$\{(9,-3),(4,-2),(1,-1),(0,0)$, $(1,1),(4,2),(9,3)\}$
In the following exercises, determine if the set of ordered pairs represents a function and if so, is the function one-to-one.$\{(-3,-5),(-2,-3),(-1,-1)$. $(0,1),(1,3),(2,5),(3,7)\}$
In the following exercises, determine if the set of ordered pairs represents a function and if so, is the function one-to-one.$\{(5,3),(4,2),(3,1),(2,0)$. $(1,-1),(0,-2),(-1,-3)\}$
In the following exercises, determine whether each graph is the graph of a function and if so, is it one-to-one.Graph a-b can't copy
In the following exercises, find the inverse of each function. Determine the domain and range of the inverse function.$\{(2,1),(4,2),(6,3),(8,4)\}$
In the following exercises, find the inverse of each function. Determine the domain and range of the inverse function.$\{(6,2),(9,5),(12,8),(15,11)\}$
In the following exercises, find the inverse of each function. Determine the domain and range of the inverse function.$\{(0,-2),(1,3),(2,7),(3,12)\}$
In the following exercises, find the inverse of each function. Determine the domain and range of the inverse function.$\{(0,0),(1,1),(2,4),(3,9)\}$
In the following exercises, find the inverse of each function. Determine the domain and range of the inverse function.$\{(-2,-3),(-1,-1),(0,1),(1,3)\}$
In the following exercises, find the inverse of each function. Determine the domain and range of the inverse function.$\{(5,3),(4,2),(3,1),(2,0)\}$
In the following exercises, graph, on the same coordinate system, the inverse of the one-to-one function shown.Graph can't copy
In the following exercises, determine whether or not the given functions are inverses.$f(x)=x+8$ and $g(x)=x-8$
In the following exercises, determine whether or not the given functions are inverses.$f(x)=x-9$ and $g(x)=x+9$
In the following exercises, determine whether or not the given functions are inverses.$f(x)=7 x$ and $g(x)=\frac{x}{7}$
In the following exercises, determine whether or not the given functions are inverses.$f(x)=\frac{x}{11}$ and $g(x)=11 x$
In the following exercises, determine whether or not the given functions are inverses.$f(x)=7 x+3$ and $g(x)=\frac{x-3}{7}$
In the following exercises, determine whether or not the given functions are inverses.$f(x)=5 x-4$ and $g(x)=\frac{x-4}{5}$
In the following exercises, determine whether or not the given functions are inverses.$f(x)=\sqrt{x+2}$ and $g(x)=x^2-2$
In the following exercises, determine whether or not the given functions are inverses.$f(x)=\sqrt[3]{x-4}$ and $g(x)=x^3+4$
In the following exercises, find the inverse of each function.$f(x)=x-12$
In the following exercises, find the inverse of each function.$f(x)=x+17$
In the following exercises, find the inverse of each function.$f(x)=9 x$
In the following exercises, find the inverse of each function.$f(x)=8 x$
In the following exercises, find the inverse of each function.$f(x)=\frac{x}{6}$
In the following exercises, find the inverse of each function.$f(x)=\frac{x}{4}$
In the following exercises, find the inverse of each function.$f(x)=6 x-7$
In the following exercises, find the inverse of each function.$f(x)=7 x-1$
In the following exercises, find the inverse of each function.$f(x)=-2 x+5$
In the following exercises, find the inverse of each function.$f(x)=-5 x-4$
In the following exercises, find the inverse of each function.$f(x)=x^2+6, \quad x \geq 0$
In the following exercises, find the inverse of each function.$f(x)=x^2-9, \quad x \geq 0$
In the following exercises, find the inverse of each function.$f(x)=x^3-4$
In the following exercises, find the inverse of each function.$f(x)=x^3+6$
In the following exercises, find the inverse of each function.$f(x)=\frac{1}{x+2}$
In the following exercises, find the inverse of each function.$f(x)=\frac{1}{x-6}$
In the following exercises, find the inverse of each function.$f(x)=\sqrt{x-2}, \quad x \geq 2$
In the following exercises, find the inverse of each function.$f(x)=\sqrt{x+8}, \quad x \geq-8$
In the following exercises, find the inverse of each function.$f(x)=\sqrt[3]{x-3}$
In the following exercises, find the inverse of each function.$f(x)=\sqrt[3]{x+5}$
In the following exercises, find the inverse of each function.$f(x)=\sqrt[4]{9 x-5}, \quad x \geq \frac{5}{9}$
In the following exercises, find the inverse of each function.$f(x)=\sqrt[4]{8 x-3}, \quad x \geq \frac{3}{8}$
In the following exercises, find the inverse of each function.$f(x)=\sqrt[5]{-3 x+5}$
In the following exercises, find the inverse of each function.$f(x)=\sqrt[5]{-4 x-3}$
Explain how the graph of the inverse of a function is related to the graph of the function.
Explain how to find the inverse of a function from its equation. Use an example to demonstrate the steps.