Find the composite functions (fo g) and (g o ). f(x) = x2 – 6 g(x) = cos(x) (fo g)(x) = (g o )(x) What is the domain of each composite function? (Enter your answers using interval notation.) domain of (f o g) domain of (g of) Are the two composite functions equal? Yes No

Q: 9-30 Find the derivative of the fun erivative. State the domain of the fu erivative. 9. f(x) = 3x –…

A: We have to find

Q: Determine the value of the constant a for which the function f(x) is continuous at - 2. x² +6x + 8…

A: Given that, f(x) is Continuous at x=-2 f(x)=x2+6x+8x+2   if x≠-2a                 if x=-2   We have…

Q: On the graph of f(x)=sinx and the domain 0≤x<2π, for which of the following intervals is f(x)…

A: We will use condition for strictly decreasing in terms of first derivative.

Q: Q1: Find and sketch the domain for each function. 1 2. f(x, y) = In(4-x²-y²) 2. f(x,y) = cos ¹(x −…

A: Given: The functions are:               1. fx,y=1ln4-x2-y2               2. fx,y=cos-1y-x2  To find:…

Q: Consider the function f defined by f(x) = x − 2 sin x on the interval [-π /4, π /2]. Find the…

A: Solution ) f(x) = x - 2sinx  Differentiate with respect to x f'(x) =  1 - 2cosx For critical point…

Q: Find f if f"(x) = 2 + cos(x), f(0) = 7, S(x/2) = -6. f(x) = x^2-cos(x)+(-(13-pi^2/4)/(pi/2))+8

A:

Q: Suppose the function f(x) has a domain of all real numbers except x = 5. The first derivative of…

A:

Q: a) Suppose F(x) is any function that is differentiable for all real numbers x. Evaluate the…

A: Given data is: To find the value of dFx3dx

Q: 2. Find the intervals of increase or decrease. a) ƒ(x)=x ln x b) f(x) = xe* c) f(x) = xe¯* d) ƒ(x) =…

A:

Q: All of the following are odd functions except:: * (A) f(x) = x (B) f(x) = 3x3 (C) f(x) = |x| (D)…

A: We know that a function f(x) is oddfunction if f(-x) = -f(x) and even if f(-x)=f(x)

Q: Find the open intervals where the function f(x)= ln(x^2+100) is concave upward or concave downward.…

A: Given function :

Q: Let g(x) = 7-2x2 be a reference function defined on the interval [-1,3] for a periodic function…

A: Let g(x) = 7-2x2 be a reference function defined on the interval [-1,3] for a periodic function…

Q: Determine where f'(x) exists, an expression for it, and where f'(x) is con- tinuous: ;x + 0 e f(x) =…

A: fx=e-1x2x, when…

Q: Find a formula for the function f(x) such that f′(x)=tan(x)/x and f(5)=5.

A: To calculate the formula for the function f(x), where the derivative of the function is defined as…

Q: 1) Find all points where f'(x) = 0. Also, graph f (x) and label the points (x, y) that you found. a)…

A: (a).   The given function is: f(x)=x3-4x2+2x-1f'(x)=03x2-8x+2=0x=4+103, x=4-103⇒x=2.387 ,  0.279…

Q: Given that f(æ) = 2x + cos(x) is one-to-one, use the formula 1 (f-1)(2) = f'(f-'(x)) to find…

A: The function fx=2x+cosx is one-to-one.

Q: 1-/1-x x2+2x x < 0 2.x4+x² 3x3+4x2 Examine the points where the function f (x) defined in real…

A:

Q: The derivative of the function f(x) = -2x2 – 16x + 24 by definition of derivatives f(r + h) – f(x)…

A:

Q: 1. Consider the function g(x) = x3 +3x2 +1. (i) Find the derivative g (x) = ?? (ii) Factor the…

A:

Q: 1) Find the value of C that make the function continuous at x=1? f(x) = { -x l6 - 2x? %3D x>1 2)…

A:

Q: Let ƒ(x) = x³ + 3x² − 9x + 22. (a) Use the definition of a derivative or the derivative rules to…

A: The given function fx=x3+3x2-9x+22 use the derivative formulas, ddxxn=nxn-1ddxax=addxa=0 where, a be…

Q: g(x) = ln x 1 f(x) = Which of the following functions are continuous for all real numbers?

A: Given The given functions are The function f(x) is continuous on interval [a,b] if it is continuous…

Q: 1.1 1.2 3 The sketch shows f(x)- asinx for xe[-90270"] -90 Determine the value of a. Sketch f(x) and…

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

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: To determine: Whether the statement is true or false. Given information: The statement is "The…

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: The function is fx=sin x+c   Let n = 1, x=π4 and c=2   Thus,  fn=f1π4=sinπ4+21=0.707+2=2.707…

Q: 1 in the form f o g. If g(x) = (x – 1), find the function f(x). Express the function h(x) x - 1

A:

Q: Verify that f = g by using a graphing utility to graph f and g in the same viewing window and (b)…

A: We graph both equations using a graphing calculator They over lie each other. So they are equal…

Q: finding the local mins and maximums and the intervals of increase and decrease and making a sign…

A:

Q: The function f is defined by f (x) = x² – 2 – 5 sin (2x). Use a calculator to find all values of x…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: The function f is defined by f (x) = x - 5 sin (2x). Use a calculator to find all values of x on the…

A: see below the answer and explanation

Q: Find the value a > 0 such that the tangent line to the graph of f(x) = x²e-3* at x = a passes…

A:

Q: Graph f(x) = 2 cos x, g(x) = cos 2x, h(x) = ( f + g)(x) in the same rectangular coordinate system…

A: fx=2cosx,  gx=cos2x,  hx=f+gx Now the graph of fx=2cosx,  gx=cos2x is,

Q: x - 5, x21 (b) A function ƒ is defined by f(x)=. 1 x<1 Show that f is differentiable at x = 1.…

A: We have to determine weather the given function is differentiable at x=1. The given function is…

Q: The domain for the function y = all real numbers except 3 and 0 ○ {x/x > 3} O less than 3 except 0…

A:

Q: Let f(x) = x³ + 9x² (a) Use the definition of a derivative or the derivative rules to find f'(x) =…

A: It is given that fx=x3+9x2-21x+20. The first derivative of fx is f'x=3x2+18x-21 and the second…

Q: Suppose the function f(x) has a domain of all real numbers and its derivative is shown below. f'(x)…

A: NOTE: Refresh your page if you can't see any equations. . the function is increasing when

Q: Given f''(x) f(0) = - 4 sin(2x) and f'(0) = 3 and 3. - Find f(G) ||

A: We will solve the problem

Q: On the graph of f(x)=sinx and the domain −2π≤x<0, for which of the following intervals is f(x)…

A: f(x)=sinx ,          domain −2π≤x&lt;0    f'(x)=cosxfirst derivative testf'(x)=0cosx=0x=-3π2 &amp;…

Q: 2. Graph the derivative of f (x) on the given graph. f(x) f'(x) Use the graphs above to make a…

A:

Q: (a) A function is labeled as, "odd" if has the property that: f(-x) = -f(x) for all values of x.…

A: Solving

Q: Suppose the function f(x) has a domain of all real numbers except x = 6. The first derivative of…

A: Given that: The function f(x) has a domain of all real number except x=6 and the derivatives of the…

Q: 7) Evaluate the limit as x approaches 3 of the function f(x) = e3-4. Then, evaluate the limit as x…

A:

Q: tan a –- 5 If f(x) : sec a f'(x) = f'(1) =

A:

Q: Let f(x) x³ + 6x² 36x +11. = (a) Use the definition of a derivative or the derivative rules to find…

A:

Q: 2 For the real-valued functions g (x)=x´+3 and h (x)=x-1, find the co %3D

A: Find the value for g(x) for x = h(x).

Q: Let f(x) = x³ + 3x² (a) Use the definition of a derivative or the derivative rules to find f'(x) =…

A:

Q: Suppose the function f(x) has a domain of all real numbers and its derivative is shown below. f'(x)…

A:

Q: Which of the following is NOT an even function?: * (A) f(x) = 3x2 (B) f(x) = |x| (C) f(x) = cos x…

A: The conditions to be even or odd for a function is: Case-1) A function is even if f-x=fx for all…

Q: 1 and g(x) 2 Let f(x) 5x + 3. - Then (f o g)(2) (ƒ o g)(x) =

A: Given query is to find the Indicated component function.

Q: Find the intervals on which f is increasing and the intervals on which it is decreasing   f(x) = -2…

A: First, we find f'(x).