Find f(2021) if the function f satisfies following conditions,(a) f(1) = 1, (b) f(x+ y) = f(x) + f(y), (c) f(-) = [closed] f(x)

Q: find f(2021) if function f satisfies following the function f(1)=1 and f(x+y)= f(x)+f(y)

A: we have given f(x+y) =f(x) +f(y) and f(1) =1. We have to find f(2021)

Q: Show that f(g)x = x - 5x  Show f(g)x = x

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Q: Let f(x) be a piecewise function defined by - 6x+ a if x - 3 What should be the values of a and b…

A: Continuity

Q: Let f(x) = (x-9)7 – 8, determine f¯¹(x). - ƒ¯¹(x) =

A: To find the inverse of the function f(x) = (x - 9)7 - 8, we need to express x in terms of y, where y…

Q: Determine the interval (s) where the following function is continuous x-7 f(x)= (x-7)x+4)

A: In the given function (x-7) is a common factor in numerator and denominator. So, it will cancel out…

Q: Let f be a function of x. Then f (10x) = 10 (f (x)). O True O False

A: the answer for the above statement is false. the explanation is given in the below step

Q: Let f : Z+ → Z be the function defined by n – 10 (F(f(n+11)) otherwise if n > 100 f(n) What is the…

A: We will find f(99)

Q: Let f(x)= x + 19 X - 16 Then f-1(x) = %3D

A:

Q: a+5 If f(z) = 3z-5 and g(z) = 3 %3D (a) f(g(z)) = (b) g(f(z)) = %3D (c) Thus g(z) is called an…

A:

Q: Let x + 2 f(x) x + 9 f-(- 9) =

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Q: The function f(z) is analytic if

A: analytic functions are functions which are locally given by the convergent power series. i.e any…

Q: represents

A: False

Q: Let f(x) = (x – 8)² + 4, æ > 8. Determine f-'(x). f-'(x) = ||

A:

Q: Let x + 1 f(x) x + 9 f-'(- 4) =

A: To find the solution first we have to find the inverse of the given function and then evaluate it at…

Q: How many fixed points are there for the function f(x)=x3

A: FInd How many fixed points are there for the function f(x)=x3.Fixed point of a function are point…

Q: 2) Let f be a function given by (3x +2 if f(x) = { 3 (x² + 1_ if Find f(0), f(-2), ƒ(-1), ƒ(1) and…

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Q: Determine the end (long run) behavior for the function below: f(x) = x - 3x³ + x – 1 Select the…

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Q: Let f(x) = 8 - x f-¹(x)

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Q: Consider the function y = (x) where f(x) = x³ +2x2 - 4x and g(x) = x2 + 2. Determine a) the domain…

A: The domain of definition of a function is a set of those values for which we can define a function.…

Q: Let f(x) f-1( – 8) = Preview

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Q: Determine a function f such that h(x) = f(g(x)), where g(x) = x + 6, and h(x) = (x+6)¹.

A: given h(x)=f(g(x))f(x)=(x+6)4  g(x)=x+6

Q: Assume that the function f is a one-to-one function. (a) If f(5) = 2, find f-'(2). Your answer is…

A: Given that to he function f is one-to-one function.

Q: Let f(x) = Vx +7 and g(x) = x +3 a) Find (2) (2) show work. b) Give the domain of the function (-)…

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Q: t) For each of the following functions, state whether they are one-to-one or not. (You must enter T…

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Q: Suppose that f(x) is a function with f( – 1) = – 9 and f(3) = 9. Determine which choice best…

A: given: we have a function f(x) such that f(-1)=-9 and f(3)=9. the given statement is: ''f(x)=0 for…

Q: Two functions f, g are defined as follows: Find a) ƒ-¹(2) b) (gof)(-4) f(x) = 3x + 5 g(x) = 2(1-x)

A:

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.