Inverse Functions

Precalculus Quiz

 





- A function f(x) is one-to-one if it does not assign the same value to two different elements of its domain.
- If f(x) is a 1-1 function, then it has an inverse function f-1 defined by f-1(y)=x if f(x)=y, for all y in the range of f.
- The domain of f-1 is the range of f, and the range of f-1 is the domain of f.
- To find a formula for f-1, we can set y = f(x), solve for x in terms of y, and set f-1(y) = x.






Question 1: Which the functions f(x), g(x) and h(x) is a one-to-one function?
f(x) = -x5
g(x) = 2x2
h(x) = |x|












Questions 2-3: If , find a formula for f-1(x) and find the domain of f-1

f-1(x):











domain of f-1:












Questions 4-5: If f(x) = 3x3 - 8, find a formula for f-1(x) and find the domain of f-1

formula for f-1(x):












domain of f-1:

















Questions 6-8: Let f(x) = x2 - 2x for x ≥ 1. Find the inverse f-1 and find the domain and the range for f-1.

formula for f-1(x):











domain of f-1:











range of f-1:












Questions 9-10: Let


Find the inverse f-1 and find the domain and the range for f-1.

formula for f-1(x):











domain of f-1:












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