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.
4
a) f(x) = x + 4
b) f(x) = 2x
c) f(x) = x + 7
x+4
d) f(x) = x – 3
e) f(x) = x3 – 1
f) f(x) = x4 – 1
g) f(x) = (x – 2)2 + 1
j) f(x) = 2x + 3
m) f(x) = x2 – 2x + 2
6.
3
k) f(x) = 2x + 3
n) f(x) = 3x2 – 6x + 1
3
i)
f(x) =
l)
f(x) = 5
x
Show that each of the following functions are inverses by showing that f(g(x)) = x.
1
1
a) f(x) = x2 – 4; g(x) = x + 4
b) f(x) = x – 1 ; g(x) = x + 1
c) f(x) = 2x + 3; g(x) =
7.
h) f(x) = x
x–3
2
2x + 1
x+1
d) f(x) = 2x – 1 ; g(x) = 2(x – 1)
ax + b
What conditions must be placed on a, b, c, and d in f(x) = cx + d 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.