Chapter 12.1, Problem 1PE

a. Given the function $f=\left\{\left(1,2\right),\left(2,3\right),\left(3,4\right)\right\}$, write the set of ordered pairs representing $f^{-1}$.

b. A necessary condition for a function $f$ to be a _____-_____-_____ function is that no two ordered pairs in $f$ have different $x$ -coordinates and the same ______-coordinate.

c. The function $f=\left\{\left(1,5\right),\left(-2,3\right),\left(-4,2\right),\left(2,5\right)\right\}$ (is/is not) a one- to- one function.

d. A function defined by $y=f\left(x\right)$ (is/is not) a one-to-one function if no horizontal line intersects the graph of $f$ in more than one point.

e. The graph of a function and its inverse are symmetric with respect to the line ________.

f. Let $f$ be a one-to-one function and let $g$ be the inverse of $f$. Then $\left(f\circ g\right)\left(x\right)=$ _____ and $\left(g\circ f\right)\left(x\right)=$ _____.

g. The notation_____ is often used to represent the inverse of a function $f$ and not the reciprocal of $f$.

h. If $\left(a,b\right)$ is a point on the graph of a one-to-one function $f$, then the corresponding ordered pair _____ is a point on the graph of $f^{-1}$.