Fog = f(g(x)) Substituting the value of g(x) in f(x) for x, we will get

Domain

Here the input function is g(x), and the denominator should not be 0. So x should not be zero. Therefore, domain is

Now let's check gof

gof = g(f(x))

Here we need to insert f(x) in g(x) for x, and on doing that , we will get

Domain

Here the input function is f(x), and denominator should not be zero.

SO domain is

Since fog = gof =x, so the given function are inverses of each other .

Ece 202: problem set 1 due: june 14, 2019 (friday) the first 3 questions of this homework assignment covers some fundamental mathematical concepts that will play a role in this course. the remaining questions are on basic signals and laplace transforms. 1. a review of complex numbers. (a) compute the magnitude and the phase of the complex numbers −4 +j, and write them in polar form (i.e., of the form rejθ). also, plot the complex number in the complex plane. (b) simplify the complex number 1 4 − √ 1 2 − j √ 2 22 and write them in cartesian form. (c) consider the complex number s = z1z2 · · ·zm p1p2 · · · pn , where each zi is a complex number with magnitude |zi | and phase ∠zi , and each pi is a complex number with magnitude |pi | and phase ∠pi . write the magnitude and phase of s in terms of the magnitudes and phases of z1, z2, . . , zm, p1, p2, . . , pn. 2. a review of differentiation. (a) find df dx for the following functions. i. f(x) = (1−4x) 2 √ x . ii. f(x) = √ 1 + tan x. (b) find dy dx for the equation e x sin y + cos2 x cos y − x 3 = 0.