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Operations with Functions

Problems

Inverse Functions

Other Methods of Finding Inverses

Problem : f (x) = 4x - 1 , g(x) = x + 1 , h(x) = (x + 1) , and j(x) = 4x + 1 . Are each of the following pairs inverse functions?
a) f and g
b) g and j
c) f and j
d) f and h

a) No.
b) No.
c) No.
d) Yes.

Problem : What is the inverse of f (x) = 5(x - 1) ?

f -1 = x + 1

Problem : What is the inverse of f (x) = 5x 2 ?

f -1 = , x≥ 0 .

Problem : If f (x) = , what is f -1 ?

f -1 = - (4x - 5) = - 4x + 5 .

Problem : What is the range of the inverse of f (x) = ?

f -1(x):f -1(x)≠-2, 0, 2, 3.

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