pt) Consider the function f: R (-co, -6) defined by fu) 3 -9 еxp(Зх + 8)...
discrete Math PLEASE CIRCLE ALL THE FINAL ANSWERS (1 pt) Consider the function f: R → R defined by f(x) = x2 + 8. Let I = (-6,3]. Describe the following sets as unions of disjoint intervals. (Hint: sketch the graph first.] f(1) = im(f) = where im(f) denotes the image (or range) off. [Syntax: use +:Inf for plus/minus infinity and the letter U for unions. For example: (-Inf-20]U(-0.5,1.5]U(3.5, Inf).] (1 pt) Consider the function f: R → (7,00) defined...
Question The function f(x) = -9 x - 8+5 8 has an inverse f-'(x) defined on the domain x < 5. Find the inverse. Provide your answer below: FEEDBACK MORE INSTRUCTION SUBMIT Content attribution
3. Consider the function defined by f(x) = 1, 0 < r< a, | 0, a< x < T, where 0a < T (a) Sketch the odd and even periodic extension of f (x) on the interval -3n < x < 3« for aT/2 (b) Find the half-range Fourier sine series expansion of f(x) for arbitrary a. (e) To what value does the half-range Fourier sine series expansion converge at r a? [8 marks 3. Consider the function defined by...
(1 pt) Consider the following two systems. (а) —Зх — 5у -4x 3y -3 -2 (b) —Зх — 5у — 4х — Зу () Find the inverse of the (common) coefficient matrix of the two systems. А1 1 3 for system (a) and 2 (i) Find the solutions to the two systems by using the inverse, i.e. by evaluating A6 where b represents the right hand side (i.e. b -2 for system (b)) 3 Solution to system (a): Solution to...
Consider the function f : R → R defined by f(x) = !x if x is rational −x if x is irrational. Find all c ∈ R at which f is continuous. Consider the function f :R → R defined by .. х if x is rational f(x) = -2 if x is irrational. Find all c ER at which f is continuous.
1. Consider the function R R defined by tz) 3+ a. Prove that onto. See Examples 227 2.29 and review the definition of conta X Y is onto if (V) ve (entre X T HS is one to one, and is a one-to-one respondence. Find the f ull b. It can also be shown that Ser Example 2.32. and R ) 2. Consider the functions : Z Q and defined to go State the domain and range of the function...
Question 8 (6 marks) Consider the function f: [-2, 2] shown in the diagram. R whose graph is (a) State the largest intervals on which f is injective f(z) (b) For each interval I you found in (a), sketch the graph of the inverse g of the restriction of f to I and state the domain and range of g (c) If we know that f(-x) = f(x) for all r e dom(f), what can we conclude about the relationship...
4. Consider the sequence of functions fu(x) = 1 timer defined on the whole real line R. f pointwise as n → for (a) (5 pts.) Find the function f such that o DE-1,1) (b) (5 pts.) Find max: (2) -f(x). Is the convergence in (a) uniform?
-/3 POINTS GHCOLALG12 3.3.052. Evaluate the piecewise-defined function. (8x if x < 0 f(x) = 9- if OS X < 8 (1x if x 28 (a) R-0.5) = (b) f(0) = (c) R(8) = Show My Work (Optional) 19. -/3 POINTS GHCOLALG12 3.3.064. Evaluate the function at the indicated x values. Rx) = [3x] (a) (6) (b) f(-4) = (c) R-1.8) - Show My Work (Optional)
In each part of this problem, the function f is defined by the formula f(x) = V[x]. (Ⓡ) Pay close attention to the domain of the function in each part and consider the statement lim f(x) = v2. ( x2 Does statement (@) make sense for the given domain? If not, why not? If statement (%) does make sense, then either prove or disprove it directly from the ε-8 definition of a limit. (a) f :R → R. (b) f...