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This printable supports Common Core Mathematics Standard HSF-BF.A.1, HSF-BF.A.1c

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Composite Functions (Grades 11-12)

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Composite Functions

1. 
Find [math](f@g)(x)[/math] if [math]f(x) = 7x + 1[/math] and [math]g(x) = -2x +34[/math].
  1. [math]-14x +35[/math]
  2. [math]-14x +239[/math]
  3. [math]5x +35[/math]
  4. [math]5x + 239[/math]
2. 
[math]f(x)= 2x+6 and g(x) = 4x+2[/math]. Find [math](g @ f)(x)[/math].
  1. [math]8x+26[/math]
  2. [math]8x+10[/math]
  3. [math]6x+8[/math]
  4. [math]6x+12[/math]
3. 
[math]f(x) =7x+9 and g(x) = 4x-1[/math]. Find [math](f @ g)(x)[/math].
  1. [math]28x+8[/math]
  2. [math]28x+16[/math]
  3. [math]28x+2[/math]
  4. [math]28x+35[/math]
4. 
[math]f(x) = 3x-12 and g(x) = 4x[/math]. Find [math](f @ g)(x)[/math].
  1. [math]12x^2+48x[/math]
  2. [math]12x-48[/math]
  3. [math]12x-12[/math]
  4. [math]7x-12[/math]
5. 
If [math]f(x)=x^2[/math] and [math]g(x)=3x-1[/math], find [math](g@f)(x)[/math].
  1. [math]x^2 +3x-1[/math]
  2. [math]9x^2 -6x+1[/math]
  3. [math]9x^2 -1[/math]
  4. [math]3x^2 -1[/math]
6. 
Let [math]f(x) = 5x-1 and g(x) = 3x^2 + 2x - 1[/math]. Find [math](g@f)(x)[/math].
  1. [math]75x^2 - 20x[/math]
  2. [math]15x^2+10x-6[/math]
  3. [math]75x^2-28x+2[/math]
  4. [math]25x-3[/math]
7. 
[math]f(x) = sqrt(x+8) and g(x)= 8x-12[/math]. Find [math](f @ g)(x)[/math].
  1. [math]2sqrt(2x-1)[/math]
  2. [math]8sqrt(x+8)-12[/math]
  3. [math]8sqrt(x-4)[/math]
  4. [math]2sqrt(2x+1)[/math]
8. 
Let [math]f(x) = 5x-2 and g(x)= (3x)/ (2+x) [/math]. Find [math](g@f)(x)[/math].
  1. [math](15x)/(x+2) - 2[/math]
  2. [math](15x)/(2+5x)[/math]
  3. [math] (3x(5x-2))/(x+2)[/math]
  4. [math](15x-6)/(5x)[/math]
9. 
[math]f(x)=6/(x-4) and g(x)= 5/(4x)[/math]. Find [math](f @ g)(x)[/math].
  1. [math](24x)/(5-16x)[/math]
  2. [math](24x)/(5+16x)[/math]
  3. [math](6x)/(5-16x)[/math]
  4. [math](5x-20)/(24x)[/math]
10. 
Let [math]f(x) = 3x^2-5x and g(x)=sqrt(x+2)[/math]. Find [math](g@f)(x)[/math].
  1. [math]3(x+2) - 5sqrt(x+2)[/math]
  2. [math]sqrt(3x^2-5x+2[/math]
  3. [math]-2x + 6[/math]
  4. [math]sqrt(3)x - (sqrt(5) -1) sqrt(x)[/math]

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