Suppose that the functions h and f are defined as follows. h (x) = 3/x, x notequalto 0 f (x) = x^2 - 1 Find the compositions h composite function h and f composite function f Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.)

Question

Mathematics

Belinda Russell

13 January, 04:12

Suppose that the functions h and f are defined as follows. h (x) = 3/x, x notequalto 0 f (x) = x^2 - 1 Find the compositions h composite function h and f composite function f Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.)

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Answers (1)

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Bruce Gardner · Answer 1

hf (x) = 3 / (x² - 1)

fh (x) = (9 - x²) / x²

Step-by-step explanation:

h (x) = 3/x

f (x) = x² - 1

h (f (x)) = 3/f (x)

hf (x) = 3 / (x² - 1)

f (h (x)) = (h (x)) ² - 1

= (3/x) ² - 1

= 9/x² - 1

fh (x) = (9 - x²) / x²