Test: Functions III - Challenging

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Question 1:   Find the inverse function of f(x)=x+2
f 1 (x)= 1 x 2
f 1 (x)= 1 x +2
f 1 (x)=x2
f 1 (x)=2x
Question 2:   Find the inverse function of f(x)= x+2 x2
f 1 (x)= 2x+2 x
f 1 (x)= 2x+2 x2
f 1 (x)= 2x+2 x1
f 1 (x)=2 x1 x+1
Question 3:   Find the inverse function of f(x)= 3( x5 ) 2( x+1 )
f 1 (x)= 2x15 2x3
f 1 (x)= 2x+15 2x3
f 1 (x)= 2x+15 2x+3
f 1 (x)= 2x+15 32x
Question 4:   Find f 1 (4) of f(x)= 2x1 53x
1
1 2
-1
3 2
Question 5:   If f(x)=2x+1 and g(x)= 1 2 x1 , find f( g(x) )
f( g(x) )=2x+2
f( g(x) )=2 1 2 x
f( g(x) )=x1
f( g(x) )= x 2 1
Question 6:   If f(x)=2x+1 and g(x)= 1 2 x1 , find g( f(x) )
g( f(x) )=x+ 1 2
g( f(x) )=x
g( f(x) )=x1 1 2
g( f(x) )=x 1 2
Question 7:   If f(x)=2x5 , g(x)= 1 3 x+3 , h(x)=5( x+1 ) find f( g( h( x ) ) )
f( g( h( x ) ) )=3 1 3 x14 1 3
f( g( h( x ) ) )=1 1 3 x2 1 6
f( g( h( x ) ) )= 1 3 x+ 2 3
f( g( h( x ) ) )=3 1 3 x 2 3
Question 8:   If f(x)=2x5 , g(x)= 1 3 x+3 , h(x)=5( x+1 ) find g( f( h( x ) ) )
g( f( h( x ) ) )=3 1 3 x2
g( f( h( x ) ) )=3 1 3 x+ 1 3
g( f( h( x ) ) )=3 1 3 x 1 3
g( f( h( x ) ) )=3 1 3 x+ 1 3
Question 9:   If f(x)= 2 5 x+7 , g(x)= 3 2 x1 find f ( g( x ) ) 1
f (g(x)) 1 =1 2 3 x+12 1 3
f (g(x)) 1 = 3 5 x+7 2 5
f (g(x)) 1 = 1 3 x+11 2 3
f (g(x)) 1 = 2 5 x+7 1 5
Question 10:   If f(x)=2x1 , g(x)=3x+2 find f ( g( 4 ) ) 1
2
1 2 3
1 1 2
1 6