F(x) = 2x + 1 and g(x) = 3x2 - 2 Find (gof)(x) Find g -1(x) if it exists Find f -1(x) if it exists

Q: F(x)=3x^2+2x-7 , G(x)=4x-5x^2+3x: Find G(x)-F(x)

A:

Q: 2) f(x) = -5x² + 3x -7, find: f(x + h)- f(x)

A: According to the problem, we have

Q: f(x) = 2x^2 + 5x+1 Use 5 long method for solution  Use 6-long method for checking of solution…

A:

Q: f(x): ×+18 and glx) = 4x-34 2. f(x) - 5x - || and glx) - 7 -3x

A:

Q: 3x-1 and g(x) За—1 f (x) = 7 x-3 ||

A: Consider the following functions: fx=3x-17gx=2x-3 gfx=2fx-3=23x-17-3=23x-1-217=23x-227=143x-22

Q: The profit function P(x) of a company selling x items is given by P(x) =-x3+9x2-15x-13 where x…

A: x is in thousands. So 6000 means x=6 x is between 0 to 6   We find the critical points of the…

Q: x² -9 f (x) = is 0<x<5 and x=33 at the point 3 x² – 2x – 3° - 1.5

A:

Q: X- f(x) = x + e¯* Solve this question by the Fixed-point method on the topic of solution of…

A: To solve : f(x)=x+e-x by fixed-point iteration method.

Q: kx +5, g(x) ={ 2 (3x+x², x<-2 If the function x2-2 is continious at x=-2, then find the value of k .

A:

Q: Detetmine all local points and all inflection points. f(x) = x⁴ - 8x³ + 18x² - 27

A: f(x) is differentiable at all points, so the stationary points are the solution of df/dx=0.

Q: 2х - 2 -1< x<0 f (x) = {-2x – 2 (5 (x+2) 0 <x<1

A:

Q: السؤال الثاني |4-x Vx-1 Find the domain of y = - 2 3+x| x+5

A: We have to find the domain of y=4-x3+x-2-x-1x+5 For domain x≠-3, x≠-5 and  x-1≥0⇒x≥1 And…

Q: Find solution using graphical method MAX Z = -2x1 - x2 subject to -3x1 - x2 = 0

A:

Q: x²-4 f(x) = In2-3x-4,

A:

Q: G(-2) if g(x) = -x^2 + 4x + 1

A:

Q: x Q3: Show that csch-¹ (²7) = coth-¹(x+¹) x-1,

A:

Q: Find a rule for g-(x) if: g(x)=3x +2 %3D g(x)=| %3D

A: For finding inverse of the function g(x) replace x by y and g(x) by x and solve for y.

Q: f(x) = x^2 - 12x + 35 g(x)= x -5 (f+g)(-4) = (f-g) (-5) =

A:

Q: (2) = 8 and f '(x) > 3 for 2 < xs7, how small can f(7) possibly be?

A: Topic:- calculus

Q: g(x) = 27x2 - x3 concave upward (-x , g) concave downward (g , x)

A:

Q: 2x +8 -5<x<-1 5. Find all x-intercepts of the function g(x)={-}x-4 -4x+10 -1<x<1 algebraically.…

A:

Q: Find all the local minima and/or maxima of the function. Show your work. f (x) = 2x3 + 5x² – 16x + 2

A:

Q: (x² +7x-7)(3x-4) (3x-1)(x²–9) 7. f(x) = Show your solution applying Quotient and product rule 8. у…

A: We have multiple question since our guideline is solve first problem only.

Q: I need help with number 21

A:

Q: Evalvate f(f(f(2) X+5 for x5

A:

Q: 1. f(x) = x², g(x) = 6-x 2. f(x) = x+ + 2x², 3. f(x) = 3+√√2x_g(x)=x-1 g(x) = 6x²

A: Since you have posted multiple subparts question in this question so i have solved the first three…

Q: f(x) = 7x3 - Vx- +7 x3 6. f(x) = 4x3-7x-2 %3D x2

A:

Q: X-2 9) f(x) = %3D x2 - x - 30

A:

Q: 8) f(x) = 2x + 5; g(x) = 3x - 1 Find bo

A: Givenf(x)=2x+5g(x)=3x-1

Q: èrentiate f(x) = [(4x³ – 1)(8x² + 6x – 3)]° and solve f'(2).

A: Given f(x)=4x3-18x2+6x-33

Q: Find (gof)(x) if f(x) = 4x and g(x) = 3x+6

A:

Q: 5. f '(x) = 7x + + – x³ find f(x) if f(0) = 7 -

A:

Q: B. Qurfient Rule ) f x)= x² 3x²

A: fx=x3-3x2x

Q: f (x) = 2x² + 3x – 4, g(x) = 2x – 1. Find (g •f)(x) -

A: Given,          fx=2x2+3x-4          gx=2x-1

Q: f'(x) = -2xe f"(x) = (4x² – 2)e- f(4) (x) = 4e* f(3) (x) = -4xe-" (2x² – 3) (3 –12x² + 4x*)

A:

Q: Find (f-g)(x) if f(x)=sqrt16x4 and g(x)=3x3-3x-5. Choose from the answers below.…

A:

Q: Date ! الموافق find the equatlon F(X) 4x + 6 X- 6x -5 ab 2 2 F(X)_4x?

A: The given function is:f(x)=4x2+6x2-6x-5To find the equation of tangent line at x=-6

Q: |3D ] B3(a): Find the critical points of the function f(x)= 7x² – 14x.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: f(x)= -4x g(x)=3x-2 h(x)=x^2-6x. solve: f(x)+g(x)

A: To find the f(x)+g(x)

Q: f)-\2+1 x>-5 3x-2 xS-5 find f(-5) and f(3). x +1 x>-5

A: For f(-5)    at x=-5  first function is given so put x=-5  in first function. And for f(3)   it…

Q: x-5 If f (x) = find f (4) x2 -10x+25

A: Given, f(x)= (x-5)/(x²-10x+25) x=4

Q: if f(x)=2x-6 and g(x)=x-x^2 find the value for g(-1)

A: f(x)=2x-6g(x)=x-x2By replacing he value of x with -1

Q: f(x)=4x-3, g(x)=x+4, (f+g)(x)=

A:

Q: F(x)=1/3x^3-1/2x^2-12x+4 Domain [-4,5] F’(x)=x^2-x-12

A: To find the correct option

Q: How do you find X in this problem?

A:

Q: Find f(x) = 3x2 + 9x – 13 as x = -6

A: We have to find the value of the function f(-6).

Q: find the value of f(-1) and f(3) y={3x+1      if x<3} {x^2      if x≥3}

A:

Q: Find the value of f(x)= |3x| -2 at x =5

A: Given function is fx=3x-2. We have to find the value of fx at x=5. Substitute x=5 in fx=3x-2 and…

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.