9. [7 points) Consider the function f(x) defined by f(x) = xeAs + B if x...
Suppose that the piecewise function J is defined by f(2)= {**** -1<<3 - 3x2 + 2x + 23, 2> 3 Determine which of the following statements are true. Select the correct answer below: O f() is not continuous at I = 3 because it is not defined at I = 3. Of() is not continuous at 2 = 3 because lim f(x) does not exist. f() is not continuous at I = 3 because lim f() f(3). ->3 f(x) is...
Let f(x) = { 80 -5 if < 10 - 7+ + b if : > 10 If f(x) is a function which is continuous everywhere, then we must have b = Let f(x) = 82 - 5 if x < 10 1 - 7x +b if x > 10 If f(x) is a function which is continuous everywhere, then we must have b= -6 2-5 - 2x + b if - 1 Let f(x) if 2 - 1 There...
48 The function f is defined by f(x) = for 3 <x< 7. The function g is defined by g(x) = 2x - 4 for .X-1 a<x<b, where a and b are constants. (i) Find the greatest value of a and the least value of b which will permit the formation of the composite function gf. [2] It is now given that the conditions for the formation of gf are satisfied. (ii) Find an expression for gf(x). [1] (iii) Find...
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
Question 6 Consider the function defined over the interval 0<x<L. Extend f(x) as a function of period 2L by using an odd half-range expansion 1) Sketch the extended function over the interval -3L<XS3L. 2) Calculate the coefficients for the Fourier Series representation of the extended function. 3) Write the first 5 non-zero terms of the Fourier Series. (10 marks)
9(10pt). Determine the value of a and b that make the function f(x) 2-3 if x < -3, x? + ax - 6 if -3 <r <2, ba - 6 ifr > 2 continuous on (-00,00) I
We consider an even and periodic function of period p = 6
defined by:
Calculate f (17.75). Justify your answer.
f(x) = 2 + e-*, pour 0 < x < 3.
Question 7 (5 points) Let f(x) = 24 and -2x, x < 5 9 3 22, x > 5 Evaluate(gof)(7) A/
9. La ste) defined as follows 9. Let f(x) defined as follows: f(x) = 0 if x < -1 = 2(x + 1)/27 if - 1<x<2 = 2/9 if 2 < x < 5 = 0 otherwise. Find F(u) = f(x)dx, where u E R.
Consider the function S Ax? f(x) = - { x < 3 17 - Ax x3 Find a value of A so that the function is continuous at x = 3. - 12/17 17/12 12/17 17/3 - 17/12