Understanding Inverse Functions: Properties and Notation Explained
Two functions f and g are inverses if they satisfy: f(g(x)) = x and g(f(x)) = x If two functions f and g are inverses, then the...
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John Rhodes
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June 21, 2023
Understanding Inverse Functions: Domain and Range Relationships in Mathematics
Domain and range of inverse functions Domain of f = Range of f^-1;Range of f = Domain of f^-1 In mathematics, the inverse function is a function...
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John Rhodes
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June 21, 2023
Understanding Inverse Functions in Math: Not All Functions are Invertible.
Does every function have an inverse function? NO No, not every function has an inverse function. A function has an inverse if and only if each output...
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John Rhodes
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June 21, 2023
Understanding the Importance and Properties of Invertible Matrices in Linear Algebra
One to one (or invertible) x and y values are not repeated (passes the vertical and horizontal line test) In linear algebra, a matrix is said to...
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John Rhodes
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June 21, 2023
Master the Vertical Line Test: The Ultimate Guide to Identifying Math Functions on Graphs
What does the vertical line test tell you? If the regular function, f, is a function or not. The vertical line test is a method used to...
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John Rhodes
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June 21, 2023
Understanding One-to-One Functions with the Horizontal Line Test: A Crucial Tool in Math
What does the horizontal line test tell you? If the inverse, f-1, is a function. The horizontal line test is a mathematical tool used to determine if...
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John Rhodes
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June 21, 2023
Understanding Inverse Functions: Reflections over the Line y=x
Inverses are reflected over… y = x Inverses are reflected over the line y=x. This means that if we have a function f(x) and it has an...
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John Rhodes
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June 21, 2023
Understanding the Sign of the Derivative: Key to Analyze Function Behavior – Explained with Examples
If f'(x) is always negative (odd exponent) or always positive (even exponent)… then f is one to one and therefore it has an inverse. If f'(x) is...