1) The one-to-one functions
g
and
h
are defined as follows.
g={(-1, 0),( -0, 3), (-1, 7), (-3, 5)}
=h(x)=-3x10
Find the following.
g^-1(0)
=
h^-1(x)
=
(h°h^-1)(8)
=
2) Suppose that the relation
S
is defined as follows.
=S{(5, 8),( -0, 3), (-3, 3),( -5, 3)}
Give the domain and range of
S
.
Write your answers using set notation.
3) Suppose that the functions
r
and
s
are defined for all real numbers
x
as follows.
r(x)=x-1
s(x)=2x^2
Write the expressions for
(r+s)(x)=
and
(r*s)(x)=
and evaluate
(r-s)(2)=
4) Suppose that the functions
p
and
q
are defined as follows.
p(x)=x^2+7
q(x)= √x+8
Find the following.
(p°q)(1)=
(q°p)(1)=
5) Suppose that the function
f
is defined , for all real numbers, as follows.
f(x)={-1/2x-2 if x≠1
{-4 if x=1
Find the following.
f(-2)=
f(1)=
f(4)=
6) For each pair of functions
f
and
g
below, find
f(g(x))
and
g(f(x)
.
Then, determine whether
f
and
g
are inverses of each other.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all
x
in the domain of the composition.
You do not have to indicate the domain.)
(a) f(x)=2x
g(x)=x/2
f(g(x))=
g(f(x))=
(b) f(x)=2x+3
g(x)=x+3
/2
f(g(x))=
g(f(x))=