{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

01_hwc1SolnsODDA - for f g In the same way we nd 12 24 3 4...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
for f g . In the same way we find g f : 1 2 3 4 5 2 4 4 2 2 h g : 1 2 3 4 5 4 2 2 4 4 h h : 1 2 3 4 5 1 2 3 4 5 Note that h h is the identity map. (b) We find h ( g f ) : 1 2 3 4 5 4 2 2 4 4 and ( h g ) f : 1 2 3 4 5 4 2 2 4 4 These are the same, which is consistent with the associativity of composition , which asserts that h ( g f ) = ( h g ) f . (c) Only f and h are one to one, onto and invertible, while g is none of these things. We have seen above that h h is the identity map, so h - 1 = h . To find f - 1 , just run it backwards: since f (5) = 1, f - 1 (1) = 5. since f (1) = 2, f - 1 (2) = 1, and so on, with the result that f - 1 : 1 2 3 4 5 5 1 3 2 4 1.5 Consider the function from
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}