Show:
Evaluating functions
Evaluating Composite Functions
Application Questions
Composite Functions
100

Given the function; w(t) = −2t + 1 

Find w(−7)

w(−7)= -2(-7) +1

          = 14+1

          =15

100

Given the Functions, f(x) = 2x+3  and g(x) = x2

What is g(f(0))?

g(f(0)) = (2(0) +3)2 

            = (0 +3)2

            = (3)2

            = 9

100

Given the piecewise functions 

g(x) =   3x +5 -2r     if x < 2

             x3 +7          if x>2

at what value of x will the function be continuous

      3x +5 -2r = x3 + 7

      3(2) +5 -2r = (2)3 +7

       6 +5 - 2r = 8 +7

        11 - 2r = 15

          -2r = 4

            r = -2

100

Given the function f(x) = 3x -4

What is f(f(x))

f(f(x)) = 3(3x - 4) - 4

          = 9x - 12 - 4

          = 9x -16

  

200

Given the function f(x) = x2 +2x - 4

What is f(3)

f(3) = 32 +2(3) - 4

      = 9 +6 -4

      = 15 - 4

      = 11

200

Given the function g(a) = 3 3a − 2 

 Find g(1)

g(1) = 3 3(1) − 2

        = 3 3 − 2

       = 3 1

       = 3

200

Given the functions h(x) = 2x - 6 and g(x) = x+ 4

What is h(g(x))


h(g(x)) = 2(x+4) - 6

           = 2x +8 -6

           = 2x + 2

300

Given the f(x) = 3x - 4 and g(x) = x3+ 9

fg(2)



fg(2)= 3((22)+9) -4

       = 3(4+9) -4

       = 3(13) - 4 

       = 39 - 4

       = 35

300

Given the functions g(n) = n + 1 f (n) = n 2 - n

Find g( f (8))

g(f(8)) = ((82) -8) +1

           = (64 - 8) +1

           = (56)+1

           =57

300

Given the functions f(x) x2  and g(x) = x -4 

What is g(f(x))? Fully simplify your answer.

g(f(x)) = (x2) - 4

          = x2 - 4

400

Given the functions f(x) 2x -10 and g(x) 3x2

What is (f + g)(5)

(f - g)(5) = f(5) - g(5)

               = 2(5) -10 -  (3(25))   

               = 10 -10 -75

               = -75

400

Given the following functions 

g(x) = 3x + 3 f (x) =x3 - 3x 2

Find g( f (x))= 3(x3 - 3x 2) + 3

                   = 3x3 - 9x 2 +3

400

Given f(x) = x2 and g(x) = x - 4 

What is f(g(x))? Fully simplify your answer

f(g(x)) = (x - 4)2

          =(x -4) (x - 4)

          = x2 -4x -4x +16

          = x2 -8x +16

500

If h(x) = 4x2 -9x +5 and h(1) = 0

What is the value of h(0.5)

h(0.5) = 4(0.5)2 -9(0.5) +5

          = 4(0.25) - 4.5 +5

          = 1 - 4.5 +5

          = -3.5 +5

          = 1.5

500

Given the functions g(x) = 4x + 5 Find 

           g(g( x /3 ))

 g(g( x /3 )) = 4(4(x/3)+5)

                   =4(4x/3 +5) +5

                   = 16x/3 +20 +5

                   = 16x/3 +25

                  =  (16x +75) / 3 

500

Given the functions f(x) = x+2  g(x) = 3x and h(x) = x2 +3x -4

What is h(g(fx))

h(g(fx)) = (3(x+2))2 +3(3(x+2)) -4

            = (3x +6)2 + 3(3x +6) -4

            = 9x2 +36x +36 +9x +18 -4

            = 9x2 +45x +50