Algebra
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algebra.docx1. 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 and
below, find
and
.
Then, determine whether
and
are inverses of each other.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all in the domain of the composition.
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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