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Inverse Relations | MathHelp.com
By MathHelp.com
Here we’re asked to solve for x in the equation: log base x of 144 = 2. Notice that we have a logarithmic equation, so let’s first convert the equation to exponential form. Remember that the base of the log represents the base of the power, the right side of the equation represents the exponent, and the number inside the log represents the result, so we have x…squared…= 144. Now, to solve for x, since x is squared, we simply take the square root of both sides of the equation to get x = plus or minus 12. Remember to always use plus or minus when taking the square root of both sides of an equation. However, notice that x represents the base of the logarithm in the original problem, and the base of a logarithm cannot be negative. Therefore, x cannot be equal to negative 12. So our final answer is x = 12.
Inverse Relations and Functions
By WOWmath.org
This videos details the steps on how to find the inverse of a function.
Inverse Functions | MathHelp.com
By MathHelp.com
In this example, we’re given a relation in the form of a chart, and we’re asked to find the inverse of the relation, then graph the relation and its inverse. To find the inverse of a relation, we simply switch the x and y values in each point. In other words, the point (1, -4) becomes (-4, 1), the point (2, 0) becomes (0, 2), the point (3, 1) becomes (1, 3), and the point (6, -1) becomes (-1, 6). Next, we’re asked to graph the relation and its inverse, so let’s first graph the relation. Notice that the relation contains the points (1, -4,), (2, 0), (3, 1), and (6, -1). And the inverse of the relation contains the points (-4, 1), (0, 2), (1, 3), and (-1, 6). Finally, it’s important to understand the following relationship between the graph of a relation and its inverse. If we draw a diagonal line through the coordinate system, which is the line that has the equation y = x, notice that the relation and its inverse are mirror images of each other in this line. In other words, the inverse of a relation is the reflection of the original relation in the line y = x.
12 - What are Inverse Functions? (Part 1) - Find the Inverse of a Function & Graph
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
03 - Inverse Variation & Joint Variation - Part 1 (Hyperbolas & Inverse Square Law)
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
Matrices: Basic Matrix Operations (add, subtract, multiply by constant)
By PatrickJMT
Matrix Operations - Adding, Subtracting, and Multiplying by a constant for matrices is discussed. For more free math videos, visit http://PatrickJMT.com!
15 - What is a Logarithm (Log x) Function? (Calculate Logs, Applications, Log Bases)
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
06 - Review of Essential Trigonometry (Sin, Cos, Tangent - Trig Identities & Functions)
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
The Simple Pendulum
By The Organic Chemistry Tutor
This physics video tutorial discusses the simple harmonic motion of a pendulum. It provides the equations that you need to calculate the period, frequency, and length of a pendulum on Earth, the Moon, or another planet. This video contains plenty of examples and practice problems.
What is a Natural Log Ln(x)? - Part 1 (Logarithm w/ Base e - Euler's number)
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
01 - Direct Variation and Proportion in Algebra - Part 1 (Constant of Variation & More)
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
How To Solve Doppler Effect Physics Problems
By The Organic Chemistry Tutor
This physics video tutorial provides a basic introduction into the doppler effect of moving sound waves. it explains how to solve doppler effect problems in physics. Any time the source moves toward the observer or if the observer moves toward the source, the detected frequency will increase - that is - the observed frequency will be greater than the frequency emitted by the source. The source can be an ambulance truck or a police siren. If the source moves away from the observer or if the observer moves away from the source, the detected frequency will decrease. This video contains plenty of examples and practice problems of calculated the frequency detected by the observer.
