For the following exercises, find f−1(x) for each function.
69. f(x)=9+10x
70. f(x)=xx+2
For the following exercise, find a domain on which the function f is one-to-one and non-decreasing. Write the domain in interval notation. Then find the inverse of f restricted to that domain.
- f(x)=x2+1
- Given f(x)=x3−5 and g(x)=3√x+5 :
- Find f(g(x)) and g(f(x)).
- What does the answer tell us about the relationship between f(x) and g(x) ?
For the following exercises, use a graphing utility to determine whether each function is one-to-one.
73. f(x)=1x
74. f(x)=−3x2+x
Practice with function notation:
75. If f(5)=2, find f−1(2).
76. If f(1)=4, find f−1(4).