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Problem 5. Let f and g be R + R defined as f(x) = 2x +1 and g(x) = x3 – 2x + 1 Find go f and determine if it is bijective. If it is bijective find its inverse. (20 pts)
part b
2. Let f(x) = x + 2x + x + 2x + 1 in Zy[x]. (a) (12 points) Show that f(x) has no roots in Zs. (b) (8 points) If f(x) is not irreducible, what are the degrees of its irreducible factors? Explain. [Do not factor f (2)]
Let f(x)=(x? + 1)^(2x – 1) is a polynomial function of fifth degree. Its second derivative is f"(x) = 4(x2 + 1)(2x – 1)+8x²(2x – 1)+ 16x(x? + 1) and third derivative is f"(x) = 24x(2x – 1) +24(x + 1) +48x2. True False dy Given the equation x3 + 3 xy + y2 = 4. We find dx 2 x' + y by implicit differentiation and is to be y' = x + y2 True False Let f(x)= x...
let f(x)=x^2 -3 and g(x)=2x+3 Evaluate. f(-2) Let f(x)=
Let f(x)=2x² – 7 and let g(x) = 4x + 1. Find the given value. f(g(-3)] f(g(-3)) = (Type an integer or a decimal) Question Viewer
(1 point) Let f(x) = (2x – 10)*(x² – 3)". 10)*(z? – 3)'. Find f'(x). f'(x) = |
Let f(x) = x2 + 1 and g(x) = 2x - 5. Find a. (f+g)(x) b. (f-g)(-1) c. (fog)(-2) d. (f.g)(x) . ()
4. Let f(x) = 6-2x, 0<x 2 (a) Expand f(x) into a periodic function of period 2, ie. construct the function F(x), such that F(x)-f (x), 0xS 2, and Fx) F(x+2) for all real numbers x. (This process is called the "full-range expansion" of f(x) into a Fourier series.) Find the Fourier series of Fr). Then sketch 3 periods of Fx). (b) Expand fx) into a cosine series of period 4. Find the Fourier series and sketch 3 periods (c)...
2) Let f(x) = 3x2 - 2x +1. a. Find the average rate of change from x = 1 to x = 3 b. Find the equation of the secant line containing the points (1.f (1)) and (3,f(3)) c. Find the derivative of the function at the point x = 3 and determine the equation of the tangent line at that point.
Let f(x) = 2x – 1.9(x) = 3x, and h(x) = x2 + 1. Compute the following: (h • (gof)(x)