The function f from R to R is defined as f (x) = x²(x − 1), determine (a) whether f is one to one. (b) whether f is onto. (c) f (R⁺) and f −¹(R⁺).

Q: Let f : R → R be a function with the following property: |f (a) – f(b)| < 4|a – b| for all a, b E R.

A:

Q: Consider the functions f : A → B, g : B → A and h : B → A such that if gf = 1A and fh = 1B. Prove…

A:

Q: Consider the functions f : A → B, g : B → A and h : B → A such that if gf = 1 Ą and fh = 1B. Prove…

A:

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

A:

Q: 6x + 5 Define a functionf: R* → R as follows: for all real numbers x, f(x) = Then f is both…

A:

Q: Let A = {1,2,3}, Define the functions f: A → C and g: B → C by f(1) = 7, f(2) = 9, f(3) = 7, g(4) =…

A:

Q: Let f : R → R be a function defined by f(x) = Decide whether it is an injection, a surjection, 1+ x2…

A:

Q: Determine the zeros of the function f(x) = -x¹ + x² +1. O a) There are no zeros. O b) x = -1.27 and…

A: GIVEN POLYNOMAIAL EQUATION  f(x)=-x4 +x2 +1

Q: 1. Describe all functions f such that f(r) ar² + bx +c and f(1) = 2 and f(-1) = 6.

A:

Q: Let B = R − {3}. Define g : B → B by g(t) = 3t/(t − 3) Show that the function g is surjective.…

A: We are given that B = R − {3}. Define g : B → B by g(t) = 3t/(t − 3). We need to show that g is…

Q: Let the function f: R R be defined by f(r) = 3r -5. Prove that the function is bijective.

A:

Q: Let f : R → R be a function given by f(x) = 2x – 1 (a) Determine whether f is bijective or not. (b)…

A:

Q: 4. Let D R {-2}, let RR {3}, and let f: DR be defined by a. Prove that f is a bijection. 3x-5 f(x)=…

A:

Q: Suppose f: R → R is a function defined by f(x) = x³. (a) Find f([-1,1]) and f-¹([0, 8]). (b) Show…

A: We shall use the intermediate value theorem to answer this question

Q: let F be the function from R to R defined by: f(x) =x². Find f–¹({1})

A:

Q: Show that f : ℝ → ℝ, f(x) = 5x − 3 is a bijective function.

A: The given function is f:ℝ→ℝ defined by fx=5x-3. We say that a function f is bijective if it is both…

Q: Use the function f(r) given below to answer the questions that follow. f(r) = – 2(r+1)(r – 3) (r –…

A: The given function f(r)=-2r+1r-33(r-1)