x + 6|, if x < -1 f(x) = x² 2? — 6х + 9 - if x > - 1 x² – 3x

Q: if x 4.

A: The function gx is a piecewise defined function.

Q: Assume that a continuous function f:R → R is X- and µ-periodic, where A and u are two nonzero…

A: We know that between two rational number lies infinite many irrational number. But function is…

Q: Determine whether f is continuous at a.

A:

Q: Check if g is continuous at t=0 and t=1. If discontinuous, identify the discontinuity as remova

A: We find left hand limit and right hand limit of g at t=0 &amp;t= 1 respectively. Then check the type…

Q: g(t) = -tan² (2+) +sin (3+¹+8+³) [[// (++1)]] cot " (cosh (3+1)), ift 71 if t <0 ifo≤t≤1

A:

Q: g(t) = -tan² (2+) +sin (3+¹+8+³) [[// (++1)]] cot " (cosh (3+1)), ift 71 if t <0 ifo≤t≤1

A:

Q: Show that has a continuous extension to x = 2, and find that extension.

A:

Q: Determine if funchin hし)

A: Determine if the function is continuous or not at a. h(x)=3xx3+x2, a=0

Q: Define f(z)=Arg(z+1). Find all points of continuity. For a point of discontinuity, determine if it…

A: We know that z=x+iy where x and y real and imaginary part of the complex number.

Q: Provide an example of function f: R → R which is continuous at exactly one point and discontinuous…

A:

Q: Show that the function Arg(z) is not continuous on each point of the non-positive real axis.

A:

Q: Construct a continuous function that shows that the intervals [0,1] and [2,6] are homeomorphic

A: In the given question we have to find a continuous function from the interval [0,1] to the interval…

Q: Let (a) Show that h is a continuous function defined on all of R.

A: Given: hx=∑n=1∞1x2+n2. We have to show that h is a continuous function defined on all of R.

Q: Give an example of a continuous function f : C -> C, where f is holomorphic at 0 but no other point…

A:

Q: g(t) = tan² (2+) +sin (3+¹+8+³) [[ / (+ + 1)]] cot" " (cosh (3+-+1)), ift 71 ift <0 ifo≤t≤1

A: Explanation of the answer is as follows

Q: Suppose the function ƒ has the property that IS(x) – S()| < |x -|| for each pair of points x, t in…

A:

Q: determine the continuity of the function at a.

A: The objective of this question is to determine whether the function f(x) = 1/(x + 2) is continuous…