(c) Show that if f is entire and |2020 + if(z)| 2020 for all z, then f is a constant function.

Q: Suppose that f is a differentiable function such that f(4)=4 and f'(4)=-2. Let g(x)=f(xsquare root…

A: We first find g'(x) and then evaluate g'(4).

Q: Find the interval on which f is increasing and in which interval f is decreasing

A:

Q: For any function f(x), if g(x) =f(x2) then  is g(x)  always increasing?

A:

Q: Prove that if the function f is 1-1, then ƒ-1 is a function.

A:

Q: - Find and classify the discontinuities of the function f(x) x2 - 1

A:

Q: 1. Show algebraically that f (a) -7x +3 is a one-to-one function |

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Let f(x)= {x^2-6+12, if x≤-1/ax+b if x>-1 Find a and b such that the function f(x) is…

A:

Q: A function f is ________ when, for each x in the domain of f, f(−x) = −f(x).

A: We have to fill in the blanks: A function f is ---- when, for each x in the domain of f, f-x=-fx. We…

Q: Suppose that f(x) is a differentiable function such that f'(4)=5 and f(4)=4. If g(x)=xf(x), then…

A:

Q: Question 26

A: To determine the domian of the function.

Q: True or False The domain of (f .g) (x) consists of thenumbers x that are in the domains of both f…

A: To determine the statementThe domain of f∘g(x) consists of the numbers x that are in the domain  of…

Q: Check the continuity of the functions f given below at 1 and 2. x +1 if x < 1 f(x) = { 2x 1+ x'if x…

A:

Q: 17. Let f be the function defined by f(x) x- 2

A: Given : f(x)=|x-2| Graph the given f(x) by making a table Assume some x values and find out f(x)…

Q: Let f(x) = { 8x6 if x 10 If f(x) is a function which is continuous everywhere, then we must have b=

A:

Q: 1. Let f be the function defined by f(x)=/x+ 2 . Prove that f is one-to-one .

A: Dear student as per our rule in one session we can only solve the first three subparts of one…

Q: Let f(x) Determine a function 4 – x | y = g(x) so that f(g(x)) x + 3

A: Given f(x)=x+14-x

Q: If f is an even function, then f −1 exists.

A: Consider an even function ,f(x)=x2 For,x=±2,we have f(±2)=4 Hence, given function is not…

Q: Find the most general function F such that F'(x) – 14. x5 || - F(x) = Σ

A:

Q: 3 Sketch a graph of the function f(x) = ax(x + 3)°(x – 1) , for some positive constant a. -

A: Given, f(x)=ax(x+3)3(x-1)2 To sketch the graph of the given function f(x). The given function is not…

Q: Is the function f (x) = x³ – 3 odd, even, or neither even nor odd? - Odd Even Neither even nor odd

A: A function f(x) is even if f(-x) = f(x) for all x ∈ R. A function f(x) is odd if f(-x) = -f(x) for…

Q: If f(x) = x +2 and x = -3, then slop function is

A: Given f(x)= x+(9/x) and x=-3. We need to find the slope function.

Q: (b) Suppose f'(x) > 1 for all x > 0, and f(0) = 0. Show that f(x) > x for all x> 0.

A: We will be using mean value theorem

Q: 3. Show algebraically that the function f (x) x* – - 2x + 5 has even, odd or neither symmetry.

A: To find out that the function has even, odd or neither of these symmetry.

Q: A function f is ________ on an interval when, for any x1 and x2 in the interval, x1 &lt; x2 implies…

A: To fill: The blank of the statement. Given: The statement is "A function f is ________ on an…

Q: Suppose that f'(x) = (x + 2)(x + 1)'(x – 1) (x- 4). %3D Which of the following statements about the…

A: We will use concept of minima and maxima to solve this problem.

Q: Determine the open intervals on which the function f(x) = ∣x + 1∣ + ∣x − 1∣ is…

A: The given function is fx=x+1+x-1. Sketch the graph of fx=x+1+x-1 as shown below.

Q: Let f be a function of x. f (x) = (x – 3)4 is an even function. - O True O False

A: Solution: The objective is to determine whether the given function is even or not

Q: Let g be a piecewise-defined function given by: 7x + Vx² + 5 2х- 4 if x 3

A: Find the values at which the peicewise function g(x) is undefined.

Q: 7. If f(x)=4x-3 and h(x) = 4x² -21, find a function g such that fog=h

A: The given functions are: fx=4x-3 and hx=4x2-21

Q: If f(x) is a function that is defined for all x E R, then f (ƒ-'(x)) = = x. True False

A: A function f-1(x)  is said to be inverse of a function f(x) if the function reverses the function.…

Q: 23-24 How would you “remove the discontinuity" of f ? In other words, how would you define f(2) in…

A:

Q: Let f(x)=(x-3)/(x2-1).  What can you say about the long-term behavior of f?

A:

Q: Find the function f °g and its domain if f(x)= x-1 and g(x) = x+5

A: Domain of the function is the set of all its possible inputs for which function is defined

Q: x +1 if x 2 if 1<x<2

A:

Q: a. Show that f has a removable discontinuity at x = 3. f(x) = x²7x+12 x + 2 x = 3

A:

Q: Does there exist a function f such that f(0) = -9, f(2) = 9, and f'(x) 5 7 for all x? O Yes O No

A:

Q: Let f(x) = x + 5 and let g(x) = x^2 + 5x. Specify the domain of f(x)/g(x).

A:

Q: For functions f and g, if f and g are both even functions, then f + g is even.

A: For _____ functions f and g, if f and g are both even functions, then f+g is even

Q: Explain if the function is continuous or not for the given number a. if x>1 if x = 1 ,a=1 if x<1…

A: we have given function     we need to determine the continuity at a=1

Q: Let f(x) be the function x + 5 for x 2.

A: Let f(x)=x+5 for x&lt;-1               =cx for -1≤x≤2                =x+6 for x&gt;2 To find the…

Q: Find the domain of the function. g(x) = In(x - x2)

A: The domain is the set of values for which the function is defined or gives a real number as an…

Q: Let h(x) = f(x)g(x). If f(x) = x² + 4x – 1, 9(-2) = 3, and g'(-2) = -5, what is h' (-2)?

A: Given h(x) = f(x)g(x). ƒ(x) = x² + 4x − 1, g(−2) = 3, and g'(-2) = −5,

Q: Let f be the function defined by f (x) = 6x. On which open intervals is ƒ decreasing? %3D -2 3 <글…

A: Given that: f(x)=x33-x22-6x

Q: Is the following function continuous? x2 – 9 if x 3 if x = 3

A: The function is given by

Q: Find f such that f'(x)= 1(4)= 20.

A:

Q: let f(x)=-2x^2-x, and let g(x)=f(x)-f(-1)/x+1, x not equal to -1. find g(10).

A:

Q: Let h(x)=f(x)g(x). If f(x)=x^2+4x−1,g(−2)=3, and g′(−2)=−5, what is h′(−2)?

A: We have to find function

Q: Suppose that f(x) is a differentiable function such that f'(4)=6 and f(4)=4. If g(x)=xf(x), then…

A:

Q: 2. Let f(x) = 2x + 1 and g(x) = a. Determine the domain and range of both f(x) and g(x).

A: Given:fx=2x+1 , gx=1x-3a.Domain of fx:2x+1≥0       2x≥-1x≥-12x≤12 Domain is (-∞,12]y=2x+1x=12,…

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.