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Define H: R (1) R (1) and J: R (1) R{1} as follows. - H(x)=3(x) = x + 1 x-1 for each x R {1} Compute the compositions H. J and J. H to determine if J and H are inverses for each other. (Simplify your answers completely.) For every x in R - {1}, (H. J)(x)H(J(x)) = H x+1 +1 x-1 2x 1 Now use the definition to find J. H. - For every x in R (1), (J. H)(x) = J Thus, --Select--- ◇ the identity function on R (1), and so H and ---Select--- inverses for each other. -

Define H: R (1) R (1) and J: R (1) R{1} as follows. - H(x)=3(x) = x + 1 x-1 for each x R {1} Compute the compositions H. J and J. H to determine if J and H are inverses for each other. (Simplify your answers completely.) For every x in R - {1}, (H. J)(x)H(J(x)) = H x+1 +1 x-1 2x 1 Now use the definition to find J. H. - For every x in R (1), (J. H)(x) = J Thus, --Select--- ◇ the identity function on R (1), and so H and ---Select--- inverses for each other. -

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Define H: R (1) R (1) and J: R (1) R{1} as follows. - H(x)=3(x) = x + 1 x-1 for each x R {1} Compute the compositions H. J and J. H to determine if J and H are inverses for each other. (Simplify your answers completely.) For every x in R - {1}, (H. J)(x)H(J(x)) = H x+1 +1 x-1 2x 1 Now use the definition to find J. H. - For every x in R (1), (J. H)(x) = J Thus, --Select--- ◇ the identity function on R (1), and so H and ---Select--- inverses for each other. -
Transcribed Image Text:Define H: R (1) R (1) and J: R (1) R{1} as follows. - H(x)=3(x) = x + 1 x-1 for each x R {1} Compute the compositions H. J and J. H to determine if J and H are inverses for each other. (Simplify your answers completely.) For every x in R - {1}, (H. J)(x)H(J(x)) = H x+1 +1 x-1 2x 1 Now use the definition to find J. H. - For every x in R (1), (J. H)(x) = J Thus, --Select--- ◇ the identity function on R (1), and so H and ---Select--- inverses for each other. -
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