1; when x when x > 1. 2x + 1 1. Consider the function f: R → R defined by f(x) 5 - 3x A. Consider function f at the point x = 1. Is function f continuous at this point? Why or why not? B. Consider function f at a point x = a where a is less than 1. Is function f continuous at this point? Why or why not? C. Consider function f at a point x = a where a is greater than 1. Is function f continuous at this point? Why or why not?

Q: 3. Let f be a function from X into Y. Suppose A and B are subsets of X. Prove that f(A U B) = f(A) U…

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Q: A function f(x) = x" – x, n > 0 is not one-to-one function.

A: As:-    A function is called one to one (injective) if distinct elements of          A are Mapped…

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A: topic - functions and continuity

Q: Consider f : R → R given by f(x) = x². What are the domain, codomain and range of f?

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Q: x² -x-2 Is the function f(x) : Fcontinuous at x = 2? Why or why not? x-2

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Q: 2. Consider the functions g, h: R → R defined by g(x) = x² and h(x) = x³ + 1. A. Evaluate f(g(x) ·…

A: g(x)=x2h(x)=x3+1∫xndx=xn+1n+1+c

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Q: Consider the function f(x) that is described by the statment: “ the function decreases to the point…

A: Explanation of the answer is as follows

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Q: Consider the function below. fx, Y) = /2 + x - y? (a) Find the domain of f. O x - y?1 2 0 oy? 2x Ox2…

A: Introduction: A two-variable function z=f(x,y) maps each ordered pair (x,y) in a subset D of the…

Q: (e) 2= /-(x + y)². (f) z -(x² + y² + 3). (g) z = 1 - ม

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Q: Which of the functions shown below is differentiable at x = -3? Select the correct answer below:

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Q: Vhich of the following best describes the function below? S (x) = * -4 ifx<2 |Vx-2 if 2sx A.…

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Q: Determine whether the function f : R → R defined by f(x) = e" is surjective. If not, determine its…

A: A function is said to be surjective/onto when range is equal to codomain of function. Given function…

Q: Refer to the function: f(x)=[x] dertermine f(-0.8)

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Q: Directions: Determine whether the given function is a. continuous or not b. differentiable or not.…

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Q: 4 For what value(s) of x is the function f(x) 2x2- 6x | NOT continuous? A. x=0 andx= 3 B. x = 3 only…

A: We need to find points at which f(x)=42x2-6x is not continous.