do you agree with the contention that the functions f(x) = x+2 and g(x)=x2-4 /x-2 are the same in every way. Provide evidence to support your position

Q: The function f is defined by f(x) = 2x +1. Find f(5x). f(5x) = 0

A: We can find f(5x) as below.

Q: Show that f(x) = 2/x2 + 3x4 – 5x6 is an even function

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Q: The function f (x) = x4 +x2 +x is an evenfunction. Justify your answer.

A: fx=x4+x2+x A function fx is said to be an even function if f-x=fx.

Q: (a) Find the critical values and the corresponding function values. (b) State the intervals on which…

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Q: Let f(x) = x - x. What is the simplest form of , h70? h

A: Please refer to the image below

Q: Let f(x) = 12x + 11 f-¹(x) = > Next Question

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Q: Let f(x) = 2? + 3 and g(x) = 3x +5. What is f(g(-1))

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Q: On which of the following intervals is f(x) = continuous? Vx-2

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Q: Explain why f(x) satisfies the Intermediate Value Theorem. f(x)=ex - x3 - 8

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Q: 5. If f(x) = (r+ 1)(x-2) x-2 and g(x) = x+1, does f(x) = g(r)? Explain.

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Q: let f(x)= 5/x +-8/4x+1. Determine the values of x for which f(x) = -2

A: Given that f(x)=-2  We plug this and find x

Q: What is the end behavior of f(x)?

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Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.