Let f, g, and h: R R be defined by f(x) = x + 2...

 

Transcribed Image Text:

Let f, g, and h: R → R be defined by f(x) = x + 2 g(x) = h(x) = 3 Compute go f(x), fog(x),hogo f(x), and go fo f(x). (4 points) . Let S = {1,2,3,4,5) and let f, g, h:S S be the functions defined by f = {(1,2), (2,1), (3,4), (4,5), (5,3)} g= {(1,3), (2,5), (3,1), (4,2), (5,4)} h = {(1,2), (2,2), (3,4), (4,3), 5,1)} a. Find f g and go f. Are these functions equals? (3 points) b. Explain why fand g have inverses but h does not. (3 points) c. Show that (fog)-¹ = g-¹ o f-1 # f-¹ o g-¹. (3 points) Let f, g, and h: R → R be defined by f(x) = x + 2 g(x) = h(x) = 3 Compute go f(x), fog(x),hogo f(x), and go fo f(x). (4 points) . Let S = {1,2,3,4,5) and let f, g, h:S S be the functions defined by f = {(1,2), (2,1), (3,4), (4,5), (5,3)} g= {(1,3), (2,5), (3,1), (4,2), (5,4)} h = {(1,2), (2,2), (3,4), (4,3), 5,1)} a. Find f g and go f. Are these functions equals? (3 points) b. Explain why fand g have inverses but h does not. (3 points) c. Show that (fog)-¹ = g-¹ o f-1 # f-¹ o g-¹. (3 points)

Answer rating: 100% (QA)

Solution of the question Solution 1 gofx gfx gna hogo fn ad go fofce g f fx g I x 2 fogx gx 2 21 hog... View the full answer