Learn inverse functions with a visual guide to reversing inputs and outputs, the horizontal line test, domain and range swaps, and reflections across y=x. Follow a worked linear inverse, verify both compositions, and see why x² needs a restricted domain before choosing the square-root branch. Save for algebra and AP Precalculus revision, then explore the matching NUM8ERS inverse functions guide.
Swap x and y, solve for the new output and use inverse notation. The input-output diagram shows how inverse functions undo each other.
Inverse Of Y 1/x
Teach Inverse Functions with this easy hand-drawn algebra infographic! Students learn how an inverse function undoes the original function using y = f⁻¹(x), with key rules like f(f⁻¹(x)) = x and f⁻¹(f(x)) = x. Includes steps for finding an inverse, swapping x and y, solving for y, graph reflection over y = x, examples, and real-life uses. Perfect for high school algebra, homeschool lessons, classroom anchor charts, functions practice, and quick revision. Save this pin to help students understand inverse functions, input-output relationships, and graphing with confidence. #InverseFunction #Functions #AlgebraBasics #MathForKids #MathEducation #HighSchoolMath #TeachingMath #Homeschooling #MathAnchorChart #StudyTips
Read about how I teach my high school students about inverse functions. Start by inverting coordinates to teach inverse functions. Notice the geometric connection with the inverse as the reflection over the line y=x. Multiple representations are explored: tables, graphs and equations. Blog post by Mathberry Lane
Inverse Of Y 6 X
The inverse of an exponential function is a logarithmic function. The inverse of a function is obtained by switching the x and y coordinates. This reflects the graph about the line y=x. As you can tell from the graph to the right, the logarithmic curve is a reflection of the exponential curve.
Re arrange the terms of the equation and integrate each side, separately. Add constant term and substitute x = 2 after integration to find the original function.
Inverse Function Of Y X
Similar to the other trig functions, the domain of tangent must be restricted for the inverse to be defined as a function. Without this, the inverse function would not pass the horizontal line test. The domain is restricted between (-pi/2, pi/2) with vertical asymptotes at these values. As a result, y=tan^-1(x) has a domain of (-∞, ∞) and a range of (-pi/2, pi/2).
The inverse function of y=sin(x) is y=sin^-1(x) and can be defined as the inverse of the restricted sine function. It is necessary to restrict the domain of sine to define the inverse. The domain of sine is restricted from -pi/2 to pi/2. The graphs of the functions y=Sin(x) and y=Sin^-1(x) are reflections of each other about the line y=x. This results in y=sin^-1(x) having a domain of -1 to 1 and a range of -pi/2 to pi/2.
One-page anchor chart/poster showing the parent + inverse graphs for quadratic/square root, cubic/cube root, and exponential/log base 2