12. Determine whether the function is one-to-one. (a) f(x) = x + 1 (b) g(x) = |x + ||

Q: 3x-4 -,x < 1 x+2 4. Given the function f (x) = . Calculate f'(1-) and f'(1+). In?x x+1

A:

Q: 7. For the function f (x)=(x-2)° +1, a. Sketch the graph of over the interval [0,3].

A:

Q: ) Find a function ƒ such that f'(x)= x³ +3 and such that the line y+5x O is tangent to the graph of…

A: Given, f'(x) = x3+3  and the line  y +5x =0 is tangent to the graph of f   Let's assume the function…

Q: 4. Is the function f(x) = (x + 1 ((x-4)² +3 ; x<4 continuous at x = 4? Why or why not? ; X24

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: Find the maximum and minimum values of the function f (x) -3x on the interval 1+x2 0<x<6.

A:

Q: x²-1 If f(x) = for x +1 and f(x)=2 when x 1, show that the function x-1 is continous at x=1?

A: Show that f is continuous at x=1

Q: 14). a) Consider the function f(x) = x – 2e-* +1 for x 2 0. i) Show that the function is increasing…

A: Note: There are multiple sub questions. No specific question has been asked. So, We will solve the…

Q: 1 If f(x) = and g(x) =-, 2x +1 1 find f (g(x)) and its domain. - 2

A: Composite function :  A composite function is created when one function is substituted into another…

Q: 3 Show that the function f(x) = - 2x + 5x has no relative extreme points. Relative extreme points…

A: Consider the function fx=13x3−2x2+5x Differentiate fx=13x3−2x2+5x with respect to x…

Q: 4. Consider the function 1/3 V3 + x f (x) X – 1 а. Find the domain of f.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 2 47) Use the graph of f(x) shown to the right to solve: a) f(x)-0 b) f(x)<0 y-f(x)

A: a) Consider the given function to be y = f(x). Solve the equation f(x) = 0 using the given graph as…

Q: Find the absolute extrema of the function on the closed interval.                          f(x) =…

A: The given function is Solve the absolute extrema on closed interval [0,4] by finding its derivative…

Q: Find the absolute extrema of the function on the closed interval. 5x f(x) [-5, 5] x2 + 16

A:

Q: What is the change of y with respect to x of the function s(x) = (3x¹ + 9x³)(x² - 6x +9) ? -9x²…

A:

Q: 9. Determine the coordinates of a point(s) that do not change between the original and the…

A: Given that: f(x)=-x2+5

Q: 10) What is the domain of the function f(x) = Eo?

A: Domain

Q: If f(x) is a differentiable function such that f'(-2)=-1 and g(x)=f(3x+1), then what is g'(-1)?

A:

Q: 5. The coordinates of the hole for the function f (x) x²-4 are: x-2

A: Given function, f(x)=x2-4x-2

Q: 21. Suppose f(x) = A and g(x) = v2*. Find the x-value for which the two functions are equal.

A:

Q: 5. Consider the function (x2 + y²)e-¯-. Provide the number of maxima of f(x, y). In case there is no…

A:

Q: 66. What will be the function g(x) resulting from normalizing the function f(x) = x³ − x4 defined in…

A: To find : function gx resulting from normalizing the function fx=x3-x4 defined in the domain 0, 34

Q: 3) Find the intervals where the function is increasing and where it is decreasing. f(x) = x² - 6x²…

A:

Q: Find the absolute extrema of the function on the closed interval. 3 f(x) = x³ – , [-1,2]

A:

Q: #2. Determine the equation for piecewise function f(x) given its graph below. -9-8-7-6-5-4-3 f(x) 5…

A: Given data:-

Q: . If x is large, which function grows faster, f1x2  2xorg1x2  x2?

A: To determine for the large values of x, which of the functions f(x)=2x and  g(x)=x2 grows faster.

Q: Find the absolute extrema of the function on the closed interval.

A: We have to find absolute extrema of the function on the given close interval: fx=x3-32x2,    -1, 2…

Q: 4. Find the functions f(x), g(x),h(x) that satisfy: f(g(h(x))) = 2.

A: A composite function is created when one function is substituted into another function .

Q: 1. Determine if the function is even or odd g(x) = x³ +x, f(t) = 1 + cost

A: Given function are gx=x3+x and ft=1+cost. To determine whether function is even or odd. Solution: A…

Q: 21. Suppose f(x) = G and g(x) = v2**. Find the x-value for which the two functions are equal.

A:

Q: III. Verify if the function is continous at the point. 1. f(x) = x³ – 2x² + x – 5 at x = 0

A: f(x) is continuous at x=0 if- limx→0-f(x)=limx→0+f(x)=f(0)

Q: What is the value for k if f(x) =x² + kr + 13 is an even function?

A:

Q: Q1: Find the value of the constant K if the function 4-x ;x#2 f (x) ={3-Vx² +5 is continuous at x=2.…

A:

Q: X+1 5) Is the function given by f(x) x2 - 8x + 15 continuous at x = 3? Why or why not?

A: f(x)=x+1x2-8x+15

Q: find the value of the constant (a, b, or c) that makes the function continuous

A:

Q: 7. Give two reasons why a function might not be differentiable at a particular value of x.

A: topic -derivative

Q: f(c) {}} [=+3 = < (3x + 1

A:

Q: Do you agree with the contention that the functions f(x) = x + 2 and g(x) = x2 − 4/x − 2 are the…

A: I am not agreed with this fact that f(x) and  g(x) are the same in every respect. The reason behind…

Q: 1. Use the second derivative test to find the relative extrema of the following function. f (x) =…

A:

Q: Q3. Determine whether the function is continuous at x=1 or not (x² - 1 x = 1 f(x)=x-1 2, x = 1

A:

Q: Locate the absolute extrema of the function f(x)=x'-12x on the closed interval [0, 3].

A:

Q: 2 a) For the function f(x) = find f' X- 3'

A:

Q: 25 Given the function f(x) = x°+ x° + x*, find all x-values where f has an inflection point.

A:

Q: 3. Do you agree with the contention that the functions f(x) = x+2 and g(x) x-2 are the same in every…

A:

Q: Find the critical and inflection points of the function f(x) = 4sin³x – 3cos²x

A:

Q: 14) What is the domain of the function f(x) E, ?

A:

Q: Find the absolute extrema of the function on the closed interval.                   f(x) = 4x / (x2…

A: f(x)= 4xx2+9so,  f1(x)= 4(x2+9) - 4x(2x)(x2+9)2Now equ    f1(x)=0=                4(x2+9) -4 x(2x) =…

Q: 6. What is a point of inflexion ? Does f(x) = x' have a point of inflexion at x = 0?

A: Given that,

Q: 3. Find the value of the constant k that makes the function continuous f(x) = {x² – 6, x + 4k, x 6

A:

Q: 1. Find the function f given that f'(x) = 2x and f(2) = 5. Is the function ƒ unique? Why?

A:

Q: 19. Find the absolute extrema of the function on the indicated interval. f (x) = xe-3x;[-1,2] хе

A: As a first step, we need to find all the critical points by equating the derivative of f(x) to zero.…