Let f(x) = x + 5 and g(x) = x2 + 9x + 20. Determine a simplified algebraic model for y = 96) and identify its domain.
Let f: R -R and g : R → Rbe some functions, and let x be a vector in R . Suppose that all the components off and g are directionally differentiable at x, and that g is such that, for all w RM, y +az) - g(y) y, w Then the composite function F(x)-g(f(x)) is directionally differentiable at x and the following chain rule holds: F, (x,d)=g'(f(x);f,(x,d)), YdER". Let f: R -R and g : R → Rbe some...
[-/1 Points] DETAILS GHCOLALG12 3.4.072. 1 Let F(x) = 1 X - 3 and g(x) = Determine the domain of the composite function. (Enter your answer using interval notation.) X-4 gof Find the composite function. (gon(x) =
2. (5 pts) Let f(x)= and x+1 5 g(x)= x-3 Find and simplify the composite function f(g(x)). Write as a single fraction.
Let f(x)=5x^2+9 and g(x)=x-4 A) Find the composite function (fog)(x) and simplify. B) Find (fog) (3)
3. Let f, g : a, b] → R be functions such that f is integrable, g is continuous. and g(x) 〉 0 for all x є a,b]. Since both f, g are bounded, let K 〉 0 be such that |f(x) K and g(x) < K for all x E [a,b (a) Let n > 0 be given. Prove that there is a partition P of [a, b such that for all i 2. (b) Let P be a...
3. Let f, g : a, bl → R be functions such that f is integrable, g is continuous. and g(x) >0 for al x E [a, b]. Since both f,g are bounded, let K> 0 be such that f(x)| 〈 K and g(x)-K for all x E la,b] (a) Let η 〉 0 be given. Prove that there is a partition P of a,b] such that for all i (b) Let P be a partition as in (a). Prove...
Let X have probability density function f(2)= k(1+x) -3 for 0 < x < oo and f(x) = 0 elsewhere. a. Find the constant k and Find the c.d.f. of X. b. Find the expected value and the variance of X. Are both well defined? c. Suppose you are required to generate a random variable X with the probability density function f(x). You have available to you a computer program that will generate a random variable U having a U[0,...
10) Let f(x) = logą (x + 3) a) Determine the Domain and the Range. b) Determine the x and y intercepts, if any. c) Determine the asymptores, if any. d) Without using a calculator plot 2 extra points and graph the function.
3. Let f, g : [a,b] → R be functions such that f is integrable, g is continuous, and g(x) >0 for all r E [a, b] Since both f,g are bounded, let K >0 be such that lf(z)| K and g(x) K for all x E [a3] (a) Let n > 0 be given. Prove that there is a partition P of [a, b such that U (P. f) _ L(P./) < η and Mi(P4)-mi(P4) < η for all...