a. Graph f x = 2 x . (See Example 1) b. Is f a one-to-one function? c. Write the domain and range of f in interval notation. d. Graph f − 1 on the same coordinate system as f . e. Write the domain and range of f − 1 in interval notation. f. From the graph evaluate f − 1 (1), f − 1 (2), and f − 1 (4).
a. Graph f x = 2 x . (See Example 1) b. Is f a one-to-one function? c. Write the domain and range of f in interval notation. d. Graph f − 1 on the same coordinate system as f . e. Write the domain and range of f − 1 in interval notation. f. From the graph evaluate f − 1 (1), f − 1 (2), and f − 1 (4).
Solution Summary: The author explains that the function f(x)=2x is a one-to-one function.
c. Write the domain and range of f in interval notation.
d. Graph
f
−
1
on the same coordinate system as f.
e. Write the domain and range of
f
−
1
in interval notation.
f. From the graph evaluate
f
−
1
(1),
f
−
1
(2), and
f
−
1
(4).
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
Use the method of disks to find the volume of the solid that is obtained
when the region under the curve y = over the interval [4,17] is rotated
about the x-axis.
1. Find the area of the region enclosed between the curves y = x and y = x.
Sketch the region.
for the given rectangular coordinates, find two sets of polar coordinates for which 0≤θ<2π, one with r>0 and the other with r<0. (-2sqrt(3),9)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY