Is there an unbounded function f:[0,1] →R where it is discontinuous only at a single point in [0,1 ]? If so, give an example of this function and explain why it is discontinuous at only 1 point.

Q: f:R - R S6 – x2 x 2 1 x < 1 fx 4x + 1 x=1, x= -1-

A:

Q: Q2) Find the domains of the following functions. Sketch a graph of the domain, and then determine…

A: Concept Used: The domain of logarithm function includes all its positive argument values because…

Q: f: Z4 → Z5 f([a]4) [39]s if a > 0. =

A: Introduction: A well-defined function is a function that is unambiguously specified by its…

Q: Consider the following piecewise-defined function: f(x) = { 4-ax² if x ≤1 b 2x if x > 1 Find the…

A: Ans :Now we need to sketch the graph in the interval [-3,3]Firstly let's find some points on the…

Q: Which of the following statements must be true for a function that is concave up everywhere?

A: Which of the  following must be there for a function than is  concave up everywhere .

Q: Formulate a condition for f to be symmetric with respect to the point (a, 0) on the x-axis.

A:

Q: Determine whether the following function is continuous at the given point x = 3x? + 14x – 5 1 x + 3…

A:

Q: (3-x, xs1 Consider the function given by f (x) = Is the function continuous, %3D x -x+1, x>1…

A:

Q: Let f: A-XX Y be defined as f (a) = (f, (a). f2 (a)) each a A, Then f is continuous if and only if…

A:

Q: If the function f: R\{2} → R\{2} defined by f (x) = 2х+3 then the composite function х-2 fof (x) =.…

A: Use the definition of composite function f∘gx=fgx, to obtain f∘fx. fx=2x+3x-2f∘fx=ffx=f2x+3x-2

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

A:

Q: Let f be the function defined by f (x) = x³ – x² – 6x. What is the absolute maximum value of f on…

A:

Q: f(x) x² - 2x - 8 { *2-22-3 x-4 x = 4 x‡4

A:

Q: Explain why Rolle’s Theorem cannot be applied to the functionƒ(x) = | x | on the interval [-a, a]…

A: Given- fx=x To explain- why Role's theorem can not be applied in the above function. Concept Used-…

Q: Determine whether f is continuous at a = -1.

A: Given- fx=x2-1x+1   if x≠-16           if  x=1 To find- whether f is continuous at x=-1 or not.…

Q: . (a) Let f: X→ Y and g: Y→ Z be functions. Show that go f: X→ Z is a function too. (b) If f: X→ Y…

A:

Q: Is the cobb-douglas function strictly concave when a1 +a2 <1 when

A:

Q: Consider the function f with domain (-2, : 3|22 – 1| if – 2 < x < 1 2x2 + 2x – 4 f(x) = 3 if x = 1…

A: