Inverse Functions
Inverse Functions
1. Graph f(x) = x2 + 1 and its inverse. Restrict the domain of f(x) so that f–1(x) is a function.
2. Graph f(x) = x3 + 1 and its inverse. Restrict the domain of f(x) so that f–1(x) is a function.
3. Graph f(x) = x3 – 1 and its inverse. Restrict the domain of f(x) so that f–1(x) is a function.
4. Graph f(x) = |x3 – 1| and its inverse. Restrict the domain of f(x) so that f–1(x) is a function.
5. Which of the following functions are 1-1? For each of the functions find the inverse and, if necessary, restrict the domain of the original function so that the inverse is a function.
a) f(x) = x + 4 b) f(x) = 2x c) f(x) =
d) f(x) = e) f(x) = x3 – 1 f) f(x) = x4 – 1
g) f(x) = (x – 2)2 + 1 h) f(x) = i) f(x) =
j) f(x) = k) f(x) = l) f(x) = 5
m) f(x) = x2 – 2x + 2 n) f(x) = 3x2 – 6x + 1
6. Show that each of the following functions are inverses by showing that f(g(x)) = x.
a) f(x) = x2 – 4; g(x) = b) f(x) = ; g(x) = + 1
c) f(x) = 2x + 3; g(x) = d) f(x) = ; g(x) =
7. What conditions must be placed on a, b, c, and d in f(x) = so that f–1(x) = f(x)?
8. Graph the inverse of each of the following functions. Where the function is not 1-1, restrict the domain of the function so that the inverse will be a function.
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