MAT 222 ASSIGNMENT WEEK 5
1. g={(-9,-5) , (-2,1) , (0, -3) ,(1,9)}
h(x)= 3x-14
Find the following: g^-1(1)
h^-1(x)
(h∘h^-1)(-2)
2. Suppose that the relation G is defined as follows.
G={ (0,-8),(3,3),(-1,8),(8,1)}
Give the domain and range of G.
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)=2x^2
s(x)=3x
write the expressions for (r+s)(x) and (r-s)(x) and evaluate (r*s)(-1).
4. Suppose that the functions p and q are define as follows:
p(x)=x^2+8
q(x)=squareroot x+1
Find the following:
(q∘p)(4)
5.suppose that the finction h is defined, for all real numbers, as follows:
h(x) { -1/2x-1 if x <-2
{ (x-1)2 – 2 if -2 ≤ x < 2
{ -4 if x ≥ 2
Find the following: h(-1) , h(2) , h(4)
6. below is a graph of y = f(x)
Translate it to make it a graph of y= f(x-2)
7. below is a graph pf y = squareroot of x
Translate it to make it a graph of y = square rootx+1 - 2.
8. For each pair of functions
Simplify your answers as much as possible.
(Assume that your expressions are defined for all
You do not have to indicate the domain.)
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a) f(x)=x+4 g(x)=x-4
f( g(x) ) = ? g( f (x) ) = ?
f and g are inverses with each other.
F and g are not inverses of each other
(Pick one)
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b) f(x)= -1/6x , x inequality sign 0 g(x)= 1/6x , x inequality sign 0
f (g(x) ) = ? g(f(g)) = ?
f and g are inverses with each other.
F and g are not inverses of each other
(Pick one)
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