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