Suppose that the functions f and g are defined as follows. f(x) =x+3 g(x) =/5x+1 %3D Find- and f+g. Then, give their domains using interval notation. Domain of (+)(+) = 0 Domain of f+g :

Q: Find the domain of the function. G(x) = √(1 - x)

A: To find the domain of the function

Q: Find the values of x for which the function is continuous. f(x)=x3-6x2+x-3 all real numbers x > 0…

A:

Q: Suppose that the function f is defined, for all real numbers, as follows. 3x-1 if x<-1 f (x) =- -x+1…

A: Given: The Piece wise function f(x)=-3x-1If x&lt;-1-x+1If x≥-1 To find: Graph the given piece wise…

Q: Let f(x) = x³ + 2, g(x) = x- - 3, and h(x) = 8x + 3. Find the rule for the function. %3D f-g

A: Given function is : fx=x3+2gx=x2-3hx=8x+3  To find the value of fx-gxhx

Q: Find the constant a such that the function is continuous on the entire real line. 7sin x 0 = g(x) =…

A:

Q: Draw the graph of f(x) and discuss its differentiability at x = 1.

A: Given fx=x2,     x≤1x,   x&gt;1

Q: Find the open intervals on which the function is increasing or decreasing          g(x) = (x + 1)3

A: We first find g'(x)

Q: Suppose that the function g is defined on the interval -2, 2) as follows. -2 if-2<x<-1 -1 if -1<x<0…

A: Suppose that the function g is defined on the interval [-2, 2). Now we have to find the values of g…

Q: f(x)%3DX²-2x+5

A:

Q: Which of the following represents a family of quartic functions with zeros -1(order 2), 2, and 3

A:

Q: Find the domain of f(x) = 3x/(x − 1) and discuss the behavior of f near any excluded x-values.

A: Given function is f(x)=3xx-1 Since domain is the set of all those input values for which the…

Q: Determine the open intervals on which the function f(x) = √(x2 − 1) is increasing,decreasing, or…

A: f(x)=x2-1

Q: Find the intervals in which the function f(x)=x' – 3x² +4 is strictly increasing for all - хER.

A:

Q: Let: f(x)=x² +, f'(x) =2x-- 21 f"x)=2+ 1. Find x- and y- intercepts of the graph of f, if it has…

A:

Q: all values of k that would make the function f (x) continuous at x = 3. I values of k exist, submit…

A:

Q: Find all the intervals at which the given function is continuous. 1. f(x)=x^2 - 3x - 10

A: Continuity: A function is said to be continuous at if following conditions holds. 1) exists 2)…

Q: Suppose that f(x) is a differentiable function such that f(4)-5 and f(4)=4. If g(x)=2xf(x), then…

A: Given f(x) is differentiable function such that f'(4)=5 and f(4)=4. Differentiating with respect to…

Q: The graph of function f(x) = x³ – 6x² + 9x + 1 is - concave upward on O (-∞0, 2) O (-∞, ∞0) O (2,…

A: The given function is: f(x)=x3-6x2+9x+1

Q: Suppose that the function g is defined on the interval (-2, 2] as follows. -1 if -2<x<-1 if –1<x<0 g…

A:

Q: Suppose that the function f is defined, for all real numbers, as follows. -x+2 if x1 Graph the…

A: Follow the next step

Q: Find the intervals on which the given function is increasing and those on which it is decreasing.…

A: Given:- g(x) =(x-2)/(x-1)  To find:- Intervals where function increasing and decreasing

Q: find the largest domain for f(x) = (x-3)2   with an upper x bound of 8 such that the function f is…

A: fx=x-32 Differentiating with respect to x, we get f'x=2x-3 Now function is non decreasing in the…

Q: 10) Suppose that the functions f and g are defined as follows. fx) = -5x² + 2x g(x) = 3x – 2 Find()…

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

Q: If f(x) = x +2 and x = -3, then slop function is

A: Given f(x)= x+(9/x) and x=-3. We need to find the slope function.

Q: Find all values of x for which the function f(x)=(x^2+x-6)/(x^2-5x+6) is not continuous.

A: We will solve the problem.

Q: Sketch the graph of f(x) by hand and use your sketch to find the absolute and local maximum and…

A: Graph of f(x) is as follows :

Q: Suppose that f:R → R is a continuous odd function, such that 1 f(x) dx = 5 and -1 | f(x) f(x) dx =…

A:

Q: Find the open intervals on which the function f(x)=-3x2+4x+5 is increasing or decreasing.

A:

Q: Let g be a piecewise-defined function given by: 7x + Vx² + 5 2х- 4 if x 3

A: Find the values at which the peicewise function g(x) is undefined.

Q: If f(x) : = x + 9 and h(x) = 2x – 4, find a function g such that g of = h. g(x) =

A:

Q: 7. If f(x)=4x-3 and h(x) = 4x² -21, find a function g such that fog=h

A: The given functions are: fx=4x-3 and hx=4x2-21

Q: the following function is a continuous function at x=2 امرفق x² +x-6 x+ 2 x) = x2 - 4 x = 2

A:

Q: If f(x) = kx' + x² – kx +2, find k such that the graph of f contains the point (2, 12).

A:

Q: 2. If f(x) = kx' +x² – kx+2, find k such that the graph of f contains the point (2, 12).

A:

Q: For the given functions f and g, find the requested function and state its domain. f(x) = 2x - 6;…

A: f(x) = 2x - 6 g(x) = 6x - 5 We are required to find (f - g)(x) and also its domain.

Q: If the function f is continuous for all real numbers and if f (x) = when z# -2, then f (-2)= -4 B -2…

A: we will use the fact that f is continuous for all real numbers and hence we will use the definition…

Q: Find the domain of the function. g(x) = In(x - x2)

A: The domain is the set of values for which the function is defined or gives a real number as an…

Q: b. Suppose the function h is defined as h(x) = 3f(x). Determine the domain and range of h.

A: b. Given that  h(x)=3f(x) Domain of f is [0,4] and range [0,2]

Q: Find the value of k so that the function f is k-x2 x3 X< 3 continuous at x=3 and f(x) х-8

A: Given, fx = k-x2x≤3x-8x&gt;3   We have to find the value of k so that function is continuous at x =…

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: if f(x)=x/x+4 and g(x)=1/x, find f o g and its domain in interval notation.

A:

Q: Find the domain of the below function: g(x)=In(x-x²)

A: For a function, y=f(x), the set of real values of x for which f(x) is defined is called the domain…

Q: Suppose that the functions f and g are defined as follows. f(x) = /x-1 g(x) = 2x-5 %3D Find f-g and…

A:

Q: (b). Determine whether the function is continuous or discontinuous at the given x-value. x²-3 x=-5…

A: Given function is

Q: f(x) = x2 + 3x - 7 and g(x) = 2x - 1 1. If f(x) = g(x), find the value of c. 2. Suppose that f(x)…

A: i have provided solution in step2.

Q: Define g(4) for the given function so that it is continuous at x= 4. 5x - 80 g(x) = 5х - 20

A:

Q: If  f(x)=x+4 and h(x)=4x-1, find a function g such that gof=h.

A: Let, Given that,

Q: DETERMINE WHETHER THE GIVEN FUNCTION n(x) IS CONTINUOUS OR DISCONTINUOUS AT x = 2 3x² +4 n(x) = if x…

A: For function to be continuous at any point, limiting value of function at that point must be equal…

Q: Find the constant a such that the function is continuous on the entire real line. x² - a² if x * a…

A:

Q: The graph of function f(x) = x³ – 6x² + 9x + 1 is concave downward on O (-∞, 2) O (-∞, ∞) O (2, c0)…

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.