Solutions

Problem Set 10

Functions

 

 Write each expression below as the composition of two functions and identify the first as   g and the second as f  for purposes of answering

 

1)                       g(x) = x2 + 5     f(x) = √x

 

2)     | x2 + 2x + 1|  + 7    g(x) = x2 + 2x + 1    f(x) = x+7

 

3)     sin3(x)  + 1               g(x) = sin(x)           f(x) = x3 + 1

 

4)     (x2 + 2x  + 5)2 + 1     g(x) = x2 + 2x  + 5     f(x) = x2 + 1

 

5)     cos(x2)                       g(x) = x2     f(x)  =  cos(x)

 

Write one expression for what     is in each case

 

6)  f(x) = 3x2 + 1            g(x) = 9x + 1      f(g(x)) = 3(9x + 1)2 + 1

 

7)   f(x) = 3                     g(x) = x4            f(g(x)) =  3

 

8)    f(x) = 3x2                g(x) =  x4            f(g(x)) = 3x8

 

9)    f(x) = x|x| + 9          g(x) = 3               f(g(x)) = 18

 

10)    f(y) = 4y+5              g(z) = 3z2          f(g(x) ) = 12x2 + 5