Suppose that the functions r and s are defined for all real numbers x as follows. r(x) =x s (x) = 3x? Write the expressions for (s-r)(x) and (s-r)(x) and evaluate (s+r)(-1). (s - )(*) = 0 (s-r)(*) = ] (s+r)(-1) = []

Q: Use the graph of f(x) = x3 + 3x2 - 4 in the figure given to factor x3 + 3x2 - 4.

A: Given function: And the graph:

Q: Find the domain of the function. f(x) = /17-x O xIx 17), or (-*, 17) U (17, ») O xx 17}, or (17, ) O…

A: We have to find the domain of the function: fx=17-x We know for any square root function y=fx it…

Q: If f(x) 3 (5х — 3)1/3, find f-1(x) | 3 x3 f-(x) = 5 3 f-'(x) = 3 А. C. = --- 3 C. f-'(x) = 5 3 f-"…

A:

Q: If the bound of error greater than zero, the polynomial is------than the .function not equal O its…

A:

Q: Discuss the continuity of the function on the closed interval.                              g(x) =…

A: We can not have a negative value under the square root.  So,

Q: Verify the Mean value Theorem for the function f(x) = 2x2 - 8z +6 on [1, 3]

A: f(x)=2x2-8x+6  on [1,3] conditions of mean value theorem: i) f(x) is continuous at (a,b) ii) f(x) is…

Q: What is the local maximum value of the f(x) = x3 - 3x +2 on [0.5, 4]

A: We are given the function  f(x) = x3 - 3x +2 on [0.5, 4]. Here, we need to find the local maximum…

Q: If the function f (x) is continuous for all real numbers and if f (x) x²-4 when x + -2, then x+2 f…

A: f(-2) = -4

Q: 9. For |x|<1, prove that 8x 16x 24x 1-x1+x 1-x 2 8x 8x = 1+ (1 – x)? (1+x2 (1-x)? ...

A:

Q: - Find f '(x). f(x) = - 3 In x+ 11x² - 9 f '(x) = . Find f '(x) f(x) = -9-5x + 4 ex f '(x) = . Find…

A: Solve for the derivative

Q: If the function f is increasing on the intervals (-5,1) and (9,21) and decreasing on the interval…

A:

Q: Find a formula for f-(x) and (f-1)'(æ) if ƒ(x) = -V5 – x f-' (x) = (5-1)'(x) =

A:

Q: Find a number x such that x + 1 / x − 2 = 3x

A: The expression could be x+1x-2=3x or x+1x-2=3x. If the expression is x+1x-2=3x, then…

Q: What is the upper bound of the function? f (x) = 4xª 25x² – 5x = 13 = 4r4 5х -13 --- Enter your…

A: Given : f(x) = 4x⁴ - 25x² - 5x - 13

Q: Suppose that ƒ'(x) = 2x for all x. Find ƒ(2) if ƒ(0) = 0

A: Given: f(0)=0

Q: Find the constant a, such that the function is continuous on the entire real line. f(x) = {2x2,…

A:

Q: Find all possible (real number) values of p, q, and r, if any, which result in the following…

A:

Q: (a) Someone has claimed that since 14 is itself a multiple of 7, then there are more multiples of 7…

A:

Q: If f(x) has odd degree and negative leading coefficient, as x goes to -∞, then f(x) would go to

A:

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A:

Q: how that the function  f(x)=x3-3x2+3x-100 is increasing on R

A:

Q: 1. prove that if x is real number then ,[2x] =[x] +[x +1/2] when [x] denote the greatest integer…

A:

Q: 7 Find f(x) given that f (1) = =-- –- and f'(x)= 2x² 4. X. 23 114

A:

Q: . Show that there exists a real number 0 <x< 2 so that x' + 8x² – 10 = 0 -

A:

Q: 17. Find the end behavior for f(x) = -3x - 2x -7 A. x- +o, f(x) +0 x -o, /(x) - - B. x-+o, /(x) -00…

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

Q: Find the constant a such that the function is continuous on the entire real line. 8sin x If x < 0 if…

A:

Q: 1 If f(x, у, 2)- ôf then х— у—3z ду а. 1 (х- у-3-)2 b. -1 (х-у-3-)* С. 1 (х-у-3-)° d. 2 (х - у-3-)?

A: In Partial differentiation w.r.t y we treat x,z as constants.

Q: List all critical numbers  f(x)=8x^(1/3)-8x^(-2/3)

A:

Q: Suppose that a function ƒ(x) has the property that ƒ(x1 x2) = ƒ(x1) + ƒ(x2) for any two positive…

A:

Q: A³ f2 = V³ fs 3

A:

Q: Use calculus to find the critical number of f(x)= x4/4 - x3/3 -3x2+10

A:

Q: The function f(x) = 4 for x < 2 and f(x) = 4 for x 2 2 has domain of all the real numbers. To True O…

A: As we know that domain is all the value of input (x-values) for which a function can define. for…

Q: Discuss the continuity of the function f(x) = {x2 − 3x if x &lt; 22x + 4 if x ≥ 2on the closed…

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: Find critical number of f(x) = x^2-7x+8

A: Given function f(x) = x2-7x+8 The critical number is the value of x which makes derivative of f(x)…

Q: A quadratic function is given f(x) 2x^2 + x - 6. Express in standard from. Find vertex and x-and y…

A: We compare the given equation with y=ax2+bx+c So, a=2, b=1 , c=-6 At vertex : For x=-0.25 we find…

Q: Discuss the continuity of the function f(x) = {x^2 - 3x         if x &lt; 2           {2x + 4…

A:

Q: How do I find th end behavior of f(x)=-(x+1)^(2)+4

A: f(x) = -(x+1)2+4 =-x2-2x-1+4=-x2-2x+3

Q: Find all critical points of the function f(x) = x³ + 3x² them in descending order and separate them…

A: Find all critical points of the function f(x) = x³ + 3x² - 5x + 9.

Q: Show that the equation x - 17x +c = 0 has at most one solution in the interval [-2, 2]. Let f(x) = x…

A: The given equation is : fx=x3-17x+c The given equation has at most one solution in the interval…

Q: - Find all critical numbers of f(x) = 3x* + 20x – 36x²

A:

Q: Find absolute extrmum(if any) f(x)=x2-4x+5 on [-2,3]

A:

Q: 2. Use the First Derivative Test with a number line to find the local extremes of the function Ax) =…

A: Solved below

Q: Show that cosh x> 1 + x² for all x.

A: comparison