2. Consider the function. f (x) 2/5 x - 4

a.) Find the inverse of f (x) and name it g (x). Show and explain your work.

b.) Use composition to show that f (x) and g (x) are inverses of each other.

c.) Draw the graphs of f (x) and g (x) on the same coordinate plane. Explain what about your graph shows that the functions are inverses of each other.

Question

Erika Wilson

Mathematics

24 May, 19:50

2. Consider the function. f (x) 2/5 x - 4

a.) Find the inverse of f (x) and name it g (x). Show and explain your work.

b.) Use composition to show that f (x) and g (x) are inverses of each other.

c.) Draw the graphs of f (x) and g (x) on the same coordinate plane. Explain what about your graph shows that the functions are inverses of each other.

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Answers (1)

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Keshawn · Answer 1

First change f (x) to y, then switch x with y and solve for y. So, x = 2/5 y - 4. Then, x + 4 = 2/5 y, then 5/2 x + 10 = y. g (x) = 5/2 x + 10. Substitute g (x) into f (x) to get 2/5 x - 4 = 5/2 x + 10 and solve (let you figure this out). Finally, just graph the two as lines.