Find the rules for (fog)(x) and (gof)(x) and give the domain of each composite function. 1. f(x)= /x .g(x)= X-4

Q: 3. Consider the function f(x)= 2x -5x. a. Find f(-x). b. Is f(-x)= f(x) ? %3D c. Find -f(x). d. Is…

A: On solving this we will get

Q: 16. For the function g(x) = x² + x – 1, find and simplify: 9*+h)-g(x) h

A:

Q: Given the function h (x) = -v2 – x, what is h (x)?

A:

Q: For what values of c is the function given below is increasing on  (- ∞   , ∞) ?

A: We find f'(x) using chain rule

Q: Find all values of x for which the garph of f lies above the graph of g.

A: Consider the given functions. fx=4xgx=1x Put the function as f(x)>g(x).…

Q: Differentiate the following function. G(x) = 3x - 7e* G'(x) =

A: given G(x)=3x-7ex we know that                   ddxxn=nxn-1ddxex=ex

Q: A square root function is given below. h(x) = --3 - Which function opens in the same direction and…

A: Given : h(x) = -12x - 3 - 2   To find the function.

Q: Consider the function h(x), for which h(2) = -5 and h' (2) = –1. h(x) Find f' (2) for the function…

A: Given function:                                   f(x)=h(x)x   Let's take the derivative of the…

Q: Which of the following is the appropriate function used in finding the value of. V2-1 f(x) =x² -…

A: f(x) =x^2 - 2x-1

Q: Find g'(x) for the given function. g(x) = /15x

A:

Q: Q3:Discuss the behavior of the following function as x0:

A: We have to discuss the behavior of the following function as x tends to 0. So, f(x) = 0 if x <_…

Q: Find the value of constant K that makes the function below continuous at x = 2. You MUST write your…

A: Given: fx=x2-2xx-2 , x<2kx-3  ,x≥2

Q: 2. Given the function -a Show that

A: Note :-  Since you have asked multiple question As per our policy, we will solve the first question…

Q: Estimate g'(3) of the function g(t) =

A:

Q: 3. Find the local extreme points of the following function: f (x) = x3 – f(x) = x³ x² + 2x + 1

A: Differentiating with respect to x, we get Now solving the first derivative by setting it to zero,…

Q: 12. Is the function f(x) even, odd, or neither? 2x + 1

A: Given function is: fx=x22x+1 We know that a function f(x) is said to be an even function of x if…

Q: Consider the function f given below. x-81 f(x) = x+9 a) For what x-values(s) is this function not…

A:

Q: Determine the values of C for which the function below is continued at the point x=2. Cx²+2x, if x <…

A:

Q: 3) Find domain of the following functions х+4 a) f (x) = х2+2х-8

A:

Q: 2. Define the following functions: f(x) = x - 5x + 25 a.

A: From the question, it is clear that the function can take input as any real number, Therefore…

Q: Can you help me find the open interval(s) on which the following function is increasing/decreasing?…

A: We differentiate the function and get slope now we see the interval where slop is positive and where…

Q: Consider the function h : N → N given by h(n) = n + (-1)*+l.

A:

Q: 1. Is the function f(x)= x³ + x−1 even, odd, or neither?

A:

Q: e following three functions will be largest for large values of x? (A)f(x)= x2 (B)r(x)= 4-x…

A: GIVENf(x)=x2,r(x)=4-x,h(x)=x16

Q: Find the value of k, if the constant k that makes the function continuous:

A: Given,          f(x)=x2+k2if x≤4kx+12if x&gt;4

Q: The data below is for a certain function h (x) h (x) -3 21 1 3

A: The graph of h-1(x) will pass through points of (h(x),x)

Q: B. Evaluate the piecewise function below at the given values of x. if -1 1 1.f(-1) 2. f(5) 3. (e)

A:

Q: Use the quotient rule to evaluate h'(a) for the given function h(x) and a. 7x 9 - 2x Provide your…

A: A detailed solution is given below.

Q: Consider the following function: f(x)=x^3+2x^2-8x-3 b. Find the extreme values ​​of f.

A:

Q: Graph the function. f(x) =. * for x<0 x+3, for x20 Choose the correct graph below. OA. OB. OC. OD.

A: Given, fx= 18x      for  x &lt;0x+3   for   x ≥ 0  We have to graph the function.

Q: 2 Consider the function f (x) = x + 6x 3 (a) Find the domain of f (x).

A:

Q: A square root function is given below. h(x) = --3 - <-2 Which function opens in the same direction…

A: We know that, the graph of a function fx=hx+k will be k units horizontally right from the graph of…

Q: 1 g(x) 5 at x = 3 3

A: given function            g(x)=15.13xat x=3substitute x=3 in the given function

Q: Consider the function h(x), for whichh(5)=11 and h′(5)=−5. Find f′(5) for the function f(x)=h(x)/x

A: Given function is Differentiating both sides with respect to x using quotient rule of…

Q: 2. State the domain of the function f and sketch the graph. a) f(x) = ln(x – 1) + 3 b) f(x) = 2log…

A: Domain of a function is the possible inputs for the function where the function is defined. So to…

Q: The function h(x) 1 can be expressed in the form f(g(x)) where g(x) = (x + 7) and f(x) is x + 7…

A: Given ,  The function h(x) = 1/(x+7) can be express es in the form f(g(x)) where g(x) = (x + 7)  We…

Q: 11 Consider the function, f (x) 2x 1 Use the above function to complete the following table. f(x) -1…

A: Explanation of the answer is as follows

Q: Draw the graph of the function f (x) = ⌊2x⌋ from R to R.

A: We have to draw the graph of the function f (x) = ⌊2x⌋ from R to R.

Q: 3. Sketch the graph of the following functions by transforming the graph of their parent functions.…

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

Q: Consider the following function.   g(x) = 2x2 + (32/x)+8   Find the x-value(s) of the relative…

A: We find the first and second derivative using power rule. Power rule: d/dx(x^n)=n*x^(n-1)

Q: Given the piecewise function below, find the value of which makes the function continuous. -I f(x):…

A:

Q: E What is the effect on the graph of the function f(x) = 5x when f(x) is replaced with 9f(x)? A)…

A:

Q: Evaluate the function for the given values of x. h(x)= Part 1 of 5 h(-3)= Part 2 of 5 -5x+7 for x…

A: The given function,   hx=-5x+7for x≤-23x+2for -2&lt;x&lt;34for x≥3

Q: Find the domain and range of the following functions.

A:

Q: Find the domain of the given function.

A: The given function is defined when 0≤x≤1 and x≠0,x≠1.

Q: Q3 Discuss the behavior of the following function as x0:

A: Now this is a piecewise-defined function whose value is 0 for non-positive values and for positive…

Q: 3-f(x)=

A: Explanation of the answer is as follows

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

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.