Composition of Functions — Quiz Answers

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If m times x is equal to the fraction with numerator x plus 5 and denominator x minus 1 and n times x is equal to x minus 3 , which function has the same domain as open paren m circ n close paren times x ?

A
h of x is equal to the fraction with numerator 11 and denominator x minus 4
B
h of x is equal to the fraction with numerator x plus 5 and denominator 11
C
h of x is equal to the fraction with numerator 11 and denominator x minus 3
D
h of x is equal to the fraction with numerator 11 and denominator x minus 1
2
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If h of x is equal to 5 plus x and k times x is equal to 1 over x , which expression is equivalent to open paren k circ h close paren times x ?

A
5 plus open paren 5 plus x close paren
B
5 plus open paren 1 over x close paren
C
the fraction with numerator open paren 5 plus x close paren and denominator x
D
the fraction with numerator 1 and denominator open paren 5 plus x close paren
3

If u times x is equal to negative 2 x squared plus 3 and v times x is equal to 1 over x , what is the range of open paren u circ v close paren times x ?

A
open paren 3 comma infinity close paren
B
open paren 1 third comma 0 close paren
C
open paren negative infinity comma plus infinity close paren
D
open paren negative infinity comma 3 close paren
4

If f of x is equal to 3 x plus 2 and g of x is equal to x squared plus 1 , which expression is equivalent to open paren f circ g close paren times x ?

A
open paren 3 x plus 2 close paren times open paren x squared plus 1 close paren
B
3 times open paren x squared plus 1 close paren plus 2
C
open paren 3 x plus 2 close paren squared plus 1
D
3 x squared plus 1 plus 2
5

If f of x is equal to the fraction with numerator x minus 3 and denominator x and g of x is equal to 5 x minus 4 , what is the domain of open paren f circ g close paren times x ?

A
start set x such that x is not equal to 3 end set
B
start set x such that x is not equal to 0 end set
C
start set x such that x is not equal to 1 third end set
D
start set x such that x is not equal to 4 fifths end set
6

For which pair of functions is open paren f circ g close paren times x is equal to x ?

A
f of x is equal to 1 half x minus 2 and g of x is equal to 1 half x plus 2
B
f of x is equal to x squared and g of x is equal to 1 over x
C
f of x is equal to the fraction with numerator x minus 2 and denominator 3 and g of x is equal to 2 minus 3 x
D
f of x is equal to 2 over x and g of x is equal to 2 over x
7

Which description best explains the domain of open paren g circ f close paren times x ?

A
the elements in the domain of g of x for which g of f of x is defined
B
the elements in the domain of f of x for which g of f of x is defined
C
the elements in the domain of g of x for which g of f of x is not zero
D
the elements in the domain of f of x for which g of f of x is not zero
8

The domain of f of x is the set of all real values except 7 , and the domain of g of x is the set of all real values except negative 3 Which of the following describes the domain of open paren g circ f close paren times x ?

A
all real values except x is not equal to 7 and the x for which f of x is not equal to 7
B
all real values except x is not equal to 7 and the x for which f of x is not equal to negative 3
C
all real values except x is not equal to negative 3 and the x for which f of x is not equal to negative 3
D
all real values except x is not equal to negative 3 and the x for which f of x is not equal to 7
9

If p times x is equal to 2 x squared minus 4 x and q times x is equal to x minus 3 , what is open paren p circ q close paren times x ?

A
2 x squared minus 16 x plus 15
B
2 x squared minus 16 x plus 18
C
2 x squared minus 4 x plus 12
D
2 x squared minus 16 x plus 30
10

If s times x is equal to x minus 7 and t times x is equal to 4 x squared minus x plus 3 , which expression is equivalent to open paren t circ s close paren times x ?

A
4 times open paren x minus 7 close paren squared minus x minus 7 plus 3
B
open paren 4 x squared minus x plus 3 close paren minus 7
C
open paren 4 x squared minus x plus 3 close paren times open paren x minus 7 close paren
D
4 times open paren x minus 7 close paren squared minus open paren x minus 7 close paren plus 3

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