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

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Operations on Functions: Domain (Grades 11-12)

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Operations on Functions: Domain

1. 
For [math]f(x)=3x-6 and g(x)=x-2[/math], find [math](f//g)(x)[/math] and its domain.
  1. 3; all real number except x = 2
  2. 1; all real numbers
  3. 3; all real numbers
  4. -3; all real numbers except x = 3
2. 
For [math]f(x) = 4x-9[/math] and [math]g(x) = 4x^2 - 5x - 9[/math], find [math](f/g)(x)[/math] (in simplest form) and state its domain.
  1. [math]1/(x+1); \ \ x !=-1, 9/4[/math]
  2. [math](4x-9)/(4x^2 - 5x - 9); \ \ RR[/math]
  3. [math]1/(4x-9); \ \ x!= 9/4[/math]
  4. [math]1/(x+1); \ \ x!=-1[/math]
3. 
Find [math](f+g)(x)[/math], and state its domain, if [math]f(x) = -x^2 + 4x + 12[/math] and [math]g(x) = sqrt(x+2)[/math].
  1. [math]-(x-6)(x+2)^(3/2); \ \ x >= -2[/math]
  2. [math]-(x-6)(x+2)^2; \ \ RR[/math]
  3. [math]-x^2 + 5x + 14; \ \ RR[/math]
  4. [math]-x^2 + 4x + sqrt(x+2) + 12; \ \ x >=-2[/math]
4. 
If [math]f(x) = 2x+3[/math] and [math]g(x) = x / (4x-1)[/math], what is [math](f-g)(x)[/math] and its domain?
  1. [math](2x+3)/(4x-1); \ \ x != 1/4[/math]
  2. [math](8x^2 + 9x - 3)/(4x-1); \ \ x != 1/4[/math]
  3. [math](x+3)/(4x-1); \ \ x!=1/4[/math]
  4. [math](x)/(-2x+4); \ \ x!=2[/math]
5. 
If [math]f(x) = x-2[/math] and [math]g(x) = (2x^2 + 4x - 70)/(x+7)[/math], find [math](f+g)(x)[/math] in its simplest form and its domain.
  1. [math](2x^2 + 5x - 72)/(x+7); \ \ x!=-7[/math]
  2. [math]3x-12; \ \ RR[/math]
  3. [math]3x-12; \ \ x!=-7[/math]
  4. [math](3x^2 + 9x + 56)/(x+7); \ \ x!=-7[/math]
6. 
Find the function [math](f/g)(x)[/math] and its domain if [math]f(x) = sqrt(-x)[/math] and [math]g(x) = sqrt(x+5)[/math].
  1. [math](-x)/(x+5); \ \ -5 < x <= 0[/math]
  2. [math](-x)/(x+5); \ \ x!=-5[/math]
  3. [math]sqrt((-x)/(x+5)); \ \ -5 < x <= 0[/math]
  4. [math]sqrt((-x)/(x+5)); \ \ x <-5 or x >= 0[/math]
7. 
For [math]f(x) = log(x+7)[/math] and [math]g(x) = log(-x+10)[/math], find [math](f-g)(x)[/math] and its domain.
  1. [math]log(17); \ \ RR[/math]
  2. [math]log((x+7)/(-x+10)); \ \ -7 < x < 10[/math]
  3. [math]log((x+7)/(-x+10)); \ \ x!= 10[/math]
  4. [math]log(2x-3); \ \ x > 2/3[/math]
8. 
Find [math](f*g)(x)[/math] and its domain, if [math]f(x) = (6x-5)/(7x+1)[/math] and [math]g(x) = (2x+2)/(3x-6)[/math].
  1. [math](12x^2 + 2x-10)/(21x^2 - 39x - 6); \ \ x!=-1/7, 2[/math]
  2. [math](12x^2-10) / (21x^2 - 6); \ \ x!= pm sqrt(14)/7[/math]
  3. [math](12x^2 + 2x-10)/(21x^2 - 39x - 6); \ \ RR[/math]
  4. [math](8x-3)/(10x-5); \ \ x !=1/2[/math]
9. 
For [math]f(x) = 2x^2 - 9x - 5[/math] and [math]g(x) = 7x-2[/math], find [math](g/f)(x)[/math] and its domain.
  1. [math]1/(2x^2) - 7/(9x) + 2/5; \ \ x!=0[/math]
  2. [math]2x^2 -9/7x + 5/2; \ \ RR[/math]
  3. [math](7x-2)/(2x^2 - 9x - 5); \ \ x!=-1/2, 5[/math]
  4. [math](2x^2 - 5x - 9) / (7x-2); \ \ x!= 2/7[/math]
10. 
If [math]f(x) = {{:(6 , 0 <= x <4),(-x+10, 4 <= x <7),(3, 7 <= x <=10):}[/math] and [math]g(x) = 1/(x-1)[/math], find [math](f+g)(x)[/math] and its domain.
  1. [math](f+g)(x) = {{:( (6x \ - \ 5)/(x \ - \ 1) , 0 <=x<4"," \ x!=1), ((-x^2 \ + \ 11x \ - \ 9)/(x \ - \ 1), 4 <= x <7),((3x \ - \ 2)/(x \ - \ 1), 7 <= x <=10):}[/math] [math] \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [/math] [math] \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [/math] [math] \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [/math] [math] \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [/math] [math] \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [/math] [math] \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [/math] [math] \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [/math] [math] \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [/math]
  2. [math](f+g)(x) = {{:( (6)/(x \ - \ 1) , 0 <= x <4"," \ x!=1),((-x \ + \ 11)/(x \ - \ 1), 4 <= x <7),((4)/(x \ - \ 1), 7 <= x <=10):}[/math]
  3. [math](f+g)(x) = (-x^2 + 20x - 18)/(x-1); \ \ 0 <= x <= 10 " and " x!=1[/math]
  4. [math](f+g)(x) = (-x^2 + 20x - 18)/(x-1); \ \ x!=1[/math]

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