For f(x)= x and g(x) = x + 4, find a. (f o g)(x), b . the domain of fog (f o g)(X) = (Simplify your answer.) . What is the domain of fo g? The domain is ISimplify your answer Type your answer In interval notation.Use int Enter your ansyer in each of the answer boxes O Type here to search

Q: Consider the function f(x)=√1-x+6 for the d 1 Find f(x), where f¹ is the inverse off. Also state the…

A: We have to find solutions

Q: Find the intervals in which the function f(x) = x4 – 8x3 – 5 is concave up/concave down. Also find…

A: From the given problem:   fx=y=x4-8x3-5   As we know that:   a). For concave upward f''x or…

Q: Consider the following function. y = x2  divided by x2 - 36 a.) Describe the x-values at which the…

A: Given:y=x2x2-36To find:The x-values at which the function is differentiable using interval notation.…

Q: 5. For the given functions f(x) = , g(x) = x + 2, find and its domain in interval notation. x-8

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Is the function f : Z→Z defined as f(n)=n^3+2 one-to-one ?

A:

Q: Consider the function f(x) = 5 · x³3 + 5 over the interval [2, 4]. Partition the interval up into…

A: Given,  fx = 5x3+5  over the interval 2, 4 We have to partition the interval up into eight equal sub…

Q: Find the numbers at which f is discontinuous. Show your work like in Example 34 from x2, x4

A: As per our company's guideline, we need to answer only one question at a time. Please repost the…

Q: For the function x2 +3 for x 2 | Identify the discontinuities of f as removable, jump, or in…

A: Given information: The function is hx=x2+3    for  x<110-x   for  1≤x≤26x-x2  for   x>2.…

Q: (a) For what value of x does f(x) = g(x)? X= (b) For which values of x is f(x) > g(x)? For every x…

A: We can solve the problem by the criteria of interse

Q: For function f, how would you remove the discontinuity? In other words, how would you define f(5) in…

A: For continuity limit of function at a point should be equal to functional value at that point.

Q: How would you "remove the discontinuity" of f? In other words, how would you define f(4) in order to…

A: Discontinuity of f can be removed by factorisation of the numerator

Q: This exercise is based on the following functions. f(x) = x² + 5 with domain (-∞, +∞) g(x) = x – 5…

A: (a) Write the formula for the function q(x). q=vgqx=vxgxHence , qx=41−xx−5

Q: For = 16 + 2x? – x* , use analytic methods to find the exact intervals on which the function is: (a)…

A:

Q: For the real-valued functions g(x): (gh)(x) = 0 Domain of g h : x-4 and h(x) = 2x+7, find the…

A:

Q: Suppose f'(x) = xe¯x². (a) On what interval is f increasing? (Enter your answer using interval…

A: Given information  f'(x)=x*e-x2

Q: Determine the set of x-values where y = x - 4 r2 +9r+18 is continuous, using interval notation.

A:

Q: For the function g(x) in part (c), how would you "remove the discontinuity"? In other words, how…

A: First, we find limx→3g(x). We rewrite g(x) as, g(x)=(x-3)(x-1)(x-3) If x≠3 we have…

Q: Find the domain of the function. h(x) = Inx+In(2-x). Express your answer in interval notation.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: for f(x)=quare root x-2 and g(x)= x quare  find f of g(x), g of f(3) domain of f of g(x)

A: Given f(x) = √(x-2) and g(x) = x2f of g(x) is a fucnction we get by replacing x in f(x) by g(x) as…

Q: (b) Find the intervals in which the function f (x)=x* +6x' +6 is concave up/concave down. Also find…

A: When f''>0 then function cancave up when f''<0 then function cancave down

Q: find the values of the constants a and/or b needed to make the following functions continuous for…

A: To fix the values of the unknown a and b to ensure the continuity of the given function

Q: Let f(x) = Vx +7 and g(x) = x +3 a) Find (2) (2) show work. b) Give the domain of the function (-)…

A:

Q: How would you "remove the discontinuity" of f? In other words, how would you define f(3) in order to…

A: The given function is: f(x)=x2-x-6x-3

Q: (b) Find the intervals in which the function f (x) =x* – 4.x³ +2 is concave up/concave down. Also…

A:

Q: Determine what, if any, value to assign to (a) to make fcontinuous at *=a. x²- 6x + 8 f(x)= .a = 4…

A:

Q: The profit P (in dollars) from sales is given by P = -200x2 + 2200x – 4600 where x is the number of…

A:

Q: For the function f(x)= x4 - 8x², determine ll a) intervals where f is Increasing b) local and…

A: Since we only answer up to 3 sub-parts, we'll answer the first 3. Please resubmit the question and…

Q: Suppose f(x) = VT and g(x) = 5x + 20. %3D The domain of f o g is a E (Express your answer in…

A: Domain.

Q: Since the simplified numerator, > 0 for all x, we have f"(x) > o x² - 1 > 0 Ix| > and f"(x) |x| <…

A: Given that: f''(x)=4(3x2+1)(x+1)3(x-1)3

Q: Use the graph of the function y=f(x) below to answer the questions. y 5- # 3- 2+ 1- -5 -4 -3 -2 -1 4…

A: The given graph is:

Q: Find the constant a such that the function is continuous on the entire real number line. Sx³, x 9

A: The value of a = 9. First of all, consider the given function. For the function to be continuous the…

Q: Consider the function f(x) = 8+ (In(z² – 4))* What is its domain and range? (Use interval notation:…

A:

Q: List the points in the graph in the interval 0 <x<6 at which the function is not differentiable. The…

A:

Q: Determine the x-values where f(x) is discontinuous. (1+x² f(x) = { 2 – x if x 2 If there are…

A:

Q: Suppose that f(x) = x*, x 2 5, and that g(x) = Vx + 3, x > 5. Find a formula for (f • g)(x) and find…

A: fx=x4, x≥5  &amp;  gx=x+3, x≥5 Now, f∘gx=fgx=fx+3=x+34=x+32

Q: Let f(x) = e2sinx 1. Find the absolute extremum values off on the interval [7]

A: To find the extreme values of given function at given  interval.

Q: find the absolute extrema of f(x)= 4x^2-48ln(x) on the interval [.4, 5]

A: Given function is  f(x)=4x2-48ln(x) Differentiate both sides with respect to x. f'(x)=8x-48x Now,…

Q: For the real-valued functions g (x) =/2x+8 and h (x) =x-1, find the composition goh and specify its…

A: The composition g∘hx is defined as ghx.

Q: 3. For f(x) = x' + 14, find all x such that f(x) = -13.

A:

Q: Use the IVT to show that f(x) = x 3 + x takes on the value 9 for some X in [1, 2].

A: Given- fx=x3+x To use- The intermediate theorem to show that the above function takes on the value 9…

Q: 4. For each part, find a real value c that makes f continuous at x=0, if possible. If not possible,…

A: A function is continious , when at that point limit of the function exists , and thatlimit is equal…

Q: Suppose f(x) and g(x) = 2x – 8. x + 2 The domain of f og is E (Express your answer in interval…

A: First we have to find f°g(x)

Q: Develop a general rule for f(n)(x) given f (x).…

A: the function given to us is    f(x) = xn

Q: 2- Calculate the extremum point of below function and Classify it f(x) = 4 x3 + 2 v11 – x + x?

A:

Q: (b) Find the intervals in which the function f(x)=x* +4x'+7 is concave up/concave down. Also find…

A:

Q: Use interval notation to indicate where - 8 f(x) = (x – 1)(x + 3) is continuous. f is continuous on…

A:

Q: How would you "remove the discontinuity" of f ? In other words, how would you define f(4) in order…

A: Given information: The function is f(x)=x2-2x-8x-4. Calculation: Solve the f(x)=x2-2x-8x-4.…

Q: Let f(x)= 6-x and g(x)= ln(x). What is the domain of g o f(x)? Express your answer in interval…

A: This question is based on functions and definition of Natural logarithm.

Q: x' - 8 24. f(x) : x? – 4

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.