6. Suppose g(x) = 3+ Evaluate g-(-1) 2x – 3

Q: 6. Eliminate the arbitrary constants from the relation y=ax² +bx +c.

A:

Q: Find the length L of the graph of 3 ( a) f(x)=x/2 +1 for 0<x< 4

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: 5 If f(x) = x + 2, evaluate f (3k +3). k=1

A: given :f(x)=x+2∑k=15 f(k+3)

Q: 12- If f(x)=v3x , g(x)=x/5, and h(x)=6x a. f(h(g(x))) b. f(g(h(x))) c. g(f(h(x))) ·

A:

Q: if (b) Suppose that f(x) (Bx² – 3 (Вх + 2 *> 2 if Find the value of B so that f(x) is continuous…

A:

Q: What are the critical points for the function f(x) = x³ + 6x² – 36x + 7 X = - 2 and x = 6 x = 2 and…

A:

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: Suppose g'(x)=sec^2(x) and g(0) = 0. What is g(x)?

A:

Q: 4х+7 (ii) If f(x)={ 1<x<2 determine whether the function f(x) is continuous 14x² -1 2<x<4 throughout…

A: Continuity of the function

Q: Let h(x) = f (X)g(x). If f (x) = In(3x² - - 4) and g(x) = 3x – 1, what is h' (x)? Select the correct…

A: Here, the given function is: h(x)=f(x)g(x)

Q: 4 Suppose that f(x, y) = x4 + y xy

A:

Q: Suppose that f'(x) = (x − 1)³x² x + 3 Determine the interval(s) on which y = f(x) is decreasing.

A: To find out the intervals on which the function is decreasing.

Q: 6. Let (1- x2, if x 1 Find f (-1)

A: 6.  Given that , f(x) = 1-x2    ; if x≤12x+1   if x&gt;1we have to find f(-1)

Q: [3, 5]. - Calculate Rg for f(x) = 7 – x over R8

A:

Q: If g(x) = max {x, 1/x} what is g(x) when x ϵ N2 (.5)?

A:

Q: are

A: We will find the critical points.

Q: 14 7) If f(x) = T4x-5) find f"(x) %3D

A: Given function is- f(x)=14(4x-5)27We need to find f''(x)First we will find f'(x) f'(x)=ddx14(4x-5)27…

Q: 5. Eliminate the arbitrary constants from the relation y = Ae* + Bxe²*.

A:

Q: If n is positive and even, where is the graph of f(x) = xn increasing and where is it decreasing?

A: For f(x)= xn  where n is positive and even. for these type of function the general graph is given…

Q: Suppose x E R. If x³ – 4x4 + 3x3 – x² +3x – 4>0, then x2 0. - |

A: Given that x∈ℝ. We have to prove the statement "If x5-4x4+3x3-x2+3x-4≥0, then x≥0" by using…

Q: 2. If f (2) = 10 and f' (x) = x²f (x) for all x, find f"(2).

A:

Q: Suppose z is implicitly defined as a function of x, y, by means of the equation: z4+8zx=3x2+12y2…

A:

Q: 2) If g(x) =3 - 2, find g-(x). %3D H-3

A: Given,           gx=3x-3-2

Q: Let k(x)=f(x)g(x)h(x). If f(x)=−2x−3,g(x)=−3x+3, and h(x)=−3x2+x+1, what is k′(1)?

A:

Q: (8) If f(x) = x² – 3x, what is f(x +h) - f(x) =? h (x² + 2xh + h²)-3(x+h)-(x²-3x) = 2x – 3 + h (x² +…

A:

Q: 4) Show that and 4x 2 - 4x f(x) = 4x-2 4-4x are eventually fixed points for the function : 0<x<…

A: Given

Q: Find f(x) - g(x) when f(x) = 2x^2 - 4x g(x) = x^2 + 6x   x^2 - 10x   3x^2   3x^2 + 2x   x^2 + 2x

A: In a polynomial expression, the like terms are the terms with the same variables and exponents.

Q: Find (go (x), given that g(x) - e nnd f(x) -

A: Given that:gx=ex and fx=x3To find: g∘fx

Q: Graph the following functions.

A: The function: fx=-2x-1if x&lt;-11if -1≤x≤12x-1if x&gt;1

Q: Analyze the critical points of f (x) = x3 − 27x − 20.

A: Critical points of a function at which f'(x)=0 or f(x) is not defined.  f(x)=x3-27x-20 f'(x)=3x2-27…

Q: c. f(x) = (-1 if x 0 %3D

A: We need to find possible points of discontinuity.

Q: . What is F(/3) if C = 0?

A:

Q: 19) If f(x) = 3x + 1 and g(x) = 5 – x°, find g(f(x)).

A: Given:

Q: calculate M6 for f(x)=7(In(x^2)) over [1,2]

A: Given the function f(x) :

Q: 6 4 Verify that for f(x, y) = 3x°y* - 4x°y°. дх ду ду дх of

A: Given problem:-

Q: 2 The critical point for the function g(x)= X +4x is Select one: a. (4,-2) b. (-2,4) C. (2,4) d.…

A:

Q: Determine f-¹(x) if 1 (X) = Or¹(x)=x2 X+2 X-3 X-2 or¹(x) X+3 Or¹(x)= X-1 3x + 2 3x + 2 X-1 OM(x)=)…

A:

Q: 8. Suppose that 2+ V4 - x2 -2 2 If F(0) = 2, find the maximum value of F(x).

A:

Q: 10. The function g(x) = x² − kx³ − 9x² + 7x − 8 has a minimum when x value of k. = 3. Determine the

A:

Q: Consider the following. 1 ifx = if x = 1 x²- 1 F(x) =

A:

Q: f  f(x)=ln(7x^6−3x^2) and g(x)=(π3lne‾‾‾√+13log2(16))5e+x5+6x,  f′(1)=

A: f(X)=ln(7x^6-3x^2)         2nd question is not written proper please write properly and resend

Q: 30. The graph of y = x³ + 21x² – x + 1 is concave down for (a) x 7 (e) x 7.

A:

Q: 1. If f(x) = 3x + 9 and g(x)=x²-4, find: a) (fog)(x) c) (gof)(x)

A: A detailed solution is given below

Q: If G(x)= (x^4)/(x^2),then G'(5) is *

A: Using Derivatives.

Q: -8- -7 -6- 5- y = f (x) 3- -2 sy = g(x) LO 4-

A:

Q: Show that the graph of f(x)=(3-4x)/e^2x has minimum value at x=5/4.

A:

Q: .If f (x) = 5x - 2, g (x) = 2x - 3 and h (x) = x2, then (fogoh) (-1) =

A:

Q: x+2 for 4. Graph. f(x) ={-V4 – x² for -2 sxs2 (-x(x-3) for x 2 f(x)t

A: Consider the function  f(x)=12x+2                 for x&lt;2−4−x2            for−2≤x≤2−xx−3…