Determine whether function f : {N U 0} --> {N U 0} defined by f(x) = {x - 1, x + 1, if x is odd x is even is (a) One-to-one and (b) Onto.
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Work With Experts to Reach at Correct Answers![30 points. Determine the impulse response and frequency response of the system defined by the difference equation y[n] = ay[n−1] + x[n−1] assuming |a| < 1. Your answers will be a function of a. 3.30 points. Suppose you have an LTI system with impulse response h[n] = {1 n = −1, 0, 10 otherwise (a) Determine whether this LTI system is causal and/or stable. (b) Determine the output of this system to the input x[n] = cos(2πn/3 + π/6) for all n.](https://www.doubtrix.com/uploads/editor/4603478099LZJFvHUsCR.png)
![Use the graphs of f and g to answer the following. (a) Identify the domains and ranges of f and g. Domain of f : [−4, 4] [−3, 5] [−3, 3] [−2, 3] Range of f : [−2, 3] [−4, 4] [−3, 5] [−3, 3] Domain of g : [−2, 3] [−4, 4] [−3, 5] [−3, 3] Range of g : [−2, 3] [−3, 5] [−4, 4] [−3, 3] (b) Identify f(−3) and g(−3). f(−3) = g(−3) = (c) For what value(s) of x is f(x) = g(x) ? x = (d) Estimate the solution(s) of f(x) = 2. x = (e) Estimate the solutions of g(x) = 0. x = (smallest value) x = (smallest value)](https://www.doubtrix.com/uploads/editor/2073269679dfpWQIGZDd.png)
![Use the graphs of f and g to answer the following. (a) Identify the domains and ranges of f and g. Domain of f : [−4, 4] [−3, 5] [−3, 3] [−2, 3] Range of f : [−2, 3] [−4, 4] [−3, 5] [−3, 3] Domain of g : [−2, 3] [−4, 4] [−3, 5] [−3, 3] Range of g : [−2, 3] [−3, 5] [−4, 4] [−3, 3] (b) Identify f(−3) and g(−3). f(−3) = g(−3) = (c) For what value(s) of x is f(x) = g(x) ? x = (d) Estimate the solution(s) of f(x) = 2. x = (e) Estimate the solutions of g(x) = 0. x = (smallest value) x = (smallest value)](https://www.doubtrix.com/uploads/editor/8896833930hafCflvYKm.png)
