Test: Functions I - Ambitious

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Question 1:   Which of the functions is one-to-one?
f( x )=sinx,{ x:πxπ }
f( x )= x 2 ,{ x:0x+ }
f( x )=cosx,{ x: π 2 x π 2 }
f( x )= x 2 ,{ x }
Question 2:   Which of the functions is many-to-one?
f( x )=sinx,{ x: π 2 x 3 2 π }
f( x )=sinx,{ x: 3 2 π<x< 5 2 π }
f( x )=tanx,{ x:π<x<2π }
f( x )=tanx,{ x:0xπ }
Question 3:   Find the inverse of the function f( x )= x 2 3,x0
f 1 ( x )= 3 x
f 1 ( x )= x+3
f 1 ( x )= 1 x +3
f 1 ( x )= x +3
Question 4:   Find the inverse of the function f( x )= 0.3 x
f 1 ( x )= 0.3 x
f 1 ( x )= x 0.3
f 1 ( x )= log 0.3 x
f 1 ( x )=0.3logx
Question 5:   Find g( f( 3 ) ) , where f( x )= 1 3 x 2 ,g( x )=2x+3
g( f( 3 ) )=27
g( f( 3 ) )=6
g( f( 3 ) )=15
g( f( 3 ) )=9
Question 6:   Find g( f( 3 ) )=15 , where f( x )=2x+1,g( x )= 1 5 x 2 ,h( x )= 2 x
g( h( f( x ) ) )= 2 5 x 2 +1
g( h( f( x ) ) )= 2 5 x+2
g( h( f( x ) ) )= 6 5 x 2
g( h( f( x ) ) )= 4 20 x 2 +20x+5
Question 7:   Which of the following functions is even?
f( x )=sin( x )
f( x )= e x 2
f( x )= 1 x
f( x )= x 3 +1
Question 8:   Which of the following functions is odd?
f( x )=| x |
f( x )= x 3
f( x )=2
f( x )=cos( x )
Question 9:   Find the period of the function f( x )=sin( 5θ )
2π
5π
3 5 π
2 5 π
Question 10:   Find the period of the function f( x )=tan( 3θ )
2π
π
1 3 π
2 3 π