Please explain the question clearly with all the options(a Let f = C(R) such that f is an infinitesimal of order 3 with respect to x-3, as x→ 3. It's true that

Q: Suppose f: (0, 1)→ (0, 1) is a surjective monotonic function. True or false: The function f is…

A: f: 0,1→0,1 is a surjective monotonic function.

Q: prove that The function f : R → R defined by f (x) = 3x − 5 is onto and one to one

A:

Q: Let f:R-->R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a>1. Show that f…

A: Let f:R-->R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a>1. Show that…

Q: Let f : Z+ → Z be the function defined by n – 10 (F(f(n+11)) otherwise if n > 100 f(n) What is the…

A: We will find f(99)

Q: Is there a real function f(x) that is differentiable only at a point x?

A:

Q: f : A → B and g : B → C are functions such that g ◦ f is surjective, then f is surjective. (ii)  If…

A: Introduction: A function f (from set A to B) is surjective if and only if there is at least one x in…

Q: Define F : R → R and G : R → Z by the following formulas: F(x) = (x^2)/3 and G(x) = ⌊x⌋ for every x…

A:

Q: 5. Let f(x) = x-3x73. Use calculus to determine the critical numbers for the function.

A: Consider the  provided function, fx=x-3x23 Find the critical point of the critical point. Find the…

Q: of intersection(s) of the normal line to the curve y=((9x^3)/(8x+4)) wherein the slope of the curve…

A: Given: The curve equation is The line equation is  2x+y=0

Q: Define g(-5) in a way that extends g(x)= 9(-5) = x² - 25 x + 8x + 15 to be continuous at x = -5.

A: We have to define g(-5) such that g(x) is continuous at x = -5.

Q: 7. Suppose f(x) = x³ – 27x + 1. Prove that f has exactly one root (zero) in the interval [0, 2].

A:

Q: Use the function f(x) = 5x – 6 to compute and expand and simplify the following. a. f(-) = b. f(-6a)…

A:

Q: 3. Let f : R→R be a function defined by f(r) = 2x + 1. Is this function (only) injective, (only)…

A: Let us consider the function f: A→B then the function is said to be  Injective or one-one :That is…

Q: Give an example of an everywhere-continuous function h(r) that is differentiable at every real…

A:

Q: Let f: R* N+ with f(x) = [x²1; that is, f(x) returns the square of x rounded up. Characterize f in…

A: Let the function f:ℝ+→ℕ+ be defined by fx=x2. Check whether the function is injective, surjective or…

Q: 6. For each of the following, is it a well-defined function? Explain. (a) (b) (d) a: R→Z a(x) = B(n)…

A:

Q: Is the function f(x) = x + 1 from the set of integers to the set of integers onto?

A: For onto from set A to B, Every value of set B should exist atleast once in the function.

Q: Let S be the part of the graph of the function x² + y² that lies above the disk x² + y² ≤ 4. What is…

A: The surface is the part of z=x2+y2:

Q: 58. Show that if f is a function and z = x+h, then f(2) – f(x) _ f(x+ h) – f(x) Z - x h

A: This question is taken from the function in which we have to prove the given equation. We can write…

Q: Use the linut definition to Compute f(x) when f)-at. the derivative f(x) when f)-2+L

A:

Q: n a and b with f(c) = N. I thi

A: Mean value theorem: Rolles theorem If a real-valued function f is continuous on a proper  [a, b],…

Q: O is a simple zero of f(x)= secx+e2 -2 %3D Select one: True O False

A:

Q: Apply Corollary 2 to the Intermediate Value Theorem. f is a polynomial and continuous everywhere.…

A: Given that, f(-3) = 170 > 0 f(-2) = -25 < 0 f(-1) = 2 > 0 f(0) = -1 < 0 f(l) = 2 > 0…