Give examples of functions f and g such that f and g do not have limits at a point c, but such that both f+g and fg have limits at c.

Q: (d) What are the domain and range of the function y = 2ƒ(x)? (Use symbolic notation and fractions…

A: The function  has a domain  and a range .The aim is to find the domain and range of

Q: Let f be piecewise function defined as following: 22 + 2x – 323 • If r < -17, the value of f(x) is…

A: The function will be discontinues where the denominator vanishes or where the left hand limit is not…

Q: (c) What are the domain and range of the function y = f(2x)? (Use symbolic notation and fractions…

A: The function  has a domain  and a range .The aim is to find the domain and range of

Q: Draw a function f(x), defined for all real numbers x, with one local maximum and two local minimum.

A:

Q: The function f is defined for all x by, 3 f(x) = x³ 3x – 1 - - - Find all maximum or minimum points.…

A:

Q: 3. There are two conditions that must be met in order for a function to be continuous, explain those…

A: See a function is continuous at a point a when these two conditions are satisfied,i) ii) Note that…

Q: If an odd function F has one local maximum of 5 at x=3, then what else can be said about F? Explain

A: Given that F is odd function and local maximum 5 at x=3. The aim is to state the characteristics of…

Q: Prove that every function is relation but converse is not true, given the answer to supports your…

A: A function is a relation that has one and only one unique element on the range for each element in…

Q: Draw a function f(z), defined for all real numbers z, with two local maximum and one local minimum.

A: We will draw a function which has two local maximum and one local minimum.

Q: Let f(x) = x²-1 and g(x)= V15 – a Find the the natural domain o the function gof(x)

A: we have to find domain

Q: True or false: There exists a monotonic function f: R → R whose range is the set of integers. True…

A:

Q: Determine whether the statement "Between any two relative minima of f, there must be at least one…

A: Determine whether the statement "Between any two relative minima of f, there must be at least one…

Q: both an even and odd number function, then show that f(x)=0 at each point in its domain

A:

Q: Use calculus to find the absolute maximum value and the absolute minimum value, if any, of the…

A: Topic:- calculus

Q: Suppose f and g are functions with domain R. If both f and g are even but f+g is odd, then prove…

A:

Q: 9. Let f(x) be defined as the piecewise function graphed at right, and let g(x) be defined as 3.…

A:

Q: The function f  whose graph is given has a discontinuity at x=4 since  does not exist. Prove true…

A: Topic:- function

Q: Let f(x)= X-4. Sketch the graph of f and f and find the rule of f-1. 2.

A: We have to sketch the graph of the function fx=12x-4 and its inverse, also find the inverse of the…

Q: (c) Show that if f is entire and |2020 + if(z)| 2020 for all z, then f is a constant function.

A:

Q: Describe the end behavior of the graph of: ƒ (x) = −5x5 + 4x² + 12x² - 8 using limits. —

A: We check the polynomial's degree and leading coefficient to determine the end behavior. The…

Q: There does not exist a function that has infinitely many discontinuities. True False

A:

Q: Prove that “if f is decreasing, then f is injective” is true. Show your work.

A: Injective function

Q: Determine if -Graph f:IR-R such that f(x) = x²+1 is surjective -Argue if it is a surjective

A: Step 1: Step 2: Step 3: Step 4: