Test: Functions I - Ambitious

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Question 1:   Which of the functions is one-to-one?
f( x )= x 2 ,{ x }
f( x )=sinx,{ x:πxπ }
f( x )=cosx,{ x: π 2 x π 2 }
f( x )= x 2 ,{ x:0x+ }
Question 2:   Which of the functions is many-to-one?
f( x )=sinx,{ x: 3 2 π<x< 5 2 π }
f( x )=sinx,{ x: π 2 x 3 2 π }
f( x )=tanx,{ x:0xπ }
f( x )=tanx,{ x:π<x<2π }
Question 3:   Find the inverse of the function f( x )= x 2 3,x0
f 1 ( x )= x+3
f 1 ( x )= x +3
f 1 ( x )= 1 x +3
f 1 ( x )= 3 x
Question 4:   Find the inverse of the function f( x )= 0.3 x
f 1 ( x )=0.3logx
f 1 ( x )= 0.3 x
f 1 ( x )= log 0.3 x
f 1 ( x )= x 0.3
Question 5:   Find g( f( 3 ) ) , where f( x )= 1 3 x 2 ,g( x )=2x+3
g( f( 3 ) )=15
g( f( 3 ) )=6
g( f( 3 ) )=27
g( f( 3 ) )=9
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