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3. Evaluating a function involves substitution, and the document gives an example of evaluating f(x)=x^2+3x-1 when x=-2.
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2) Composition of functions including finding f(g(x)) and g(f(x)) for given functions f(x) and g(x).
3) Finding inverses of functions and verifying inverses by composition.
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3) The standard form of a quadratic equation is f(x) = a(x - h)^2 + k, where the vertex is (h, k) and the axis of symmetry is x = h.¥×¥í¥°¥é¥ß¥ó¥°Haskell 13Õ †–î}7
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1) Starting from the base case that mapping an empty list results in an empty list
2) Assuming map f (map g xs) = map (f . g) xs is true for some list xs
3) Showing through substitutions and definitions that this holds true for lists of the form x:xs as well
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1. Composition functions are not commutative.
2. They are associative.
3. Identity functions leave other functions unchanged when composed.
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3. Evaluating a function involves substitution, and the document gives an example of evaluating f(x)=x^2+3x-1 when x=-2.
4. To find the domain from the equation, one looks at what type of equation it is such as linear, absolute value, quadratic, radical, fractional, or other. The domain is the set of inputs that can be substituted into theDay 5 examples
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The document provides examples of evaluating composite functions. It gives the steps to find (f ? g)(x) by substituting the expression for g(x) into f(x) and simplifying. Examples are provided of finding (f ? g)(x) and (g ? f)(x) for various functions f(x) and g(x), as well as evaluating composite functions at given values.PC Exam 1 study guide
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2) Composition of functions including finding f(g(x)) and g(f(x)) for given functions f(x) and g(x).
3) Finding inverses of functions and verifying inverses by composition.
4) Operations on complex numbers including plotting, finding modulus, distance, midpoint, addition, subtraction, multiplication, and division.
5) Graphing functions, classifying function types, and stating domains and ranges.
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2) The derivative of a function of two variables f(x,y) at a point (a,b) is represented by the Jacobian matrix Jf(a,b), which can be written as the gradient vector grad f(a,b).
3) The directional derivative of f(x,y) at (a,b) in the direction of a unit vector u isAnalisis matematico
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This document contains solutions to mathematical problems involving functions. It defines several functions and solves for their domains, ranges, and other properties. Some key points extracted:
1) It defines functions for the areas of isosceles triangles and spheres in terms of their variables.
2) It analyzes properties of various functions like whether they are injective, surjective, or both.
3) It finds the domains and ranges of multiple functions by solving equations or looking at discontinuities.Day 5 examples u6w14
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1. The document discusses composite functions, which involve combining two functions f(x) and g(x) where the output of one is used as the input of the other. It provides examples of evaluating composite functions using tables and graphs.
2. Key steps for evaluating composite functions are: 1) Substitute the inner function into the outer function and 2) Simplify the expression. Order matters as f(g(x)) and g(f(x)) may have different values.
3. Examples are worked through to find composite functions given basic functions like f(x) = x + 1 and g(x) = 2x as well as more complex rational functions.1.6 all notes
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This document provides definitions and properties for trigonometric functions including sine, cosine, and tangent. It defines the domains and ranges of sine, cosine, and tangent. Examples of trigonometric ratios are given for common angles like 30, 45, 60, and 90 degrees. Trigonometric identities are also listed, such as the sine and cosine of sums and differences of angles.Concept map function
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