Adding and
Subtracting Functions
Subtracting Functions
How do you add and subtract functions?
** Hint: 3 words **
Combine like terms
After finding a common denominator, what operation do you do to the exponents?
Add the exponents
After finding a common denominator, what operation do you do to the exponents?
Subtract the exponents
f (x) = x + 3
h (x) = √(x – 7)
Find f(h(11))
f(h(11)) =5
How do you find the inverse of a function?
** Hint: 2 steps **
1. Switch x and y
2. Solve the equation for y
f (x) = –6√(x)
g (x) = 2√(x)
Find:
1. (f + g)(x)
2. The domain of (f + g)(x)
3. (f + g)(25)
1. (f + g)(x) = –4√(x)
2. Domain of (f + g)(x) = x ≥ 0
3. (f + g)(25) = –20
f (x) = 4x⅔
g (x) = 2x⅓
Find:
1. (fg)(x)
2. The domain of (fg)(x)
3. (fg)(–7)
1. (fg)(x) = 8x
2. Domain of (fg)(x) = All real numbers
3. (fg)(–7) = –56
f (x) = 4x5/4
g (x) = x½
Find:
1. (f/g)(x)
2. The domain of (f/g)(x)
3. (f/g)(81)
1. (f/g)(x) = 4x¾
2. Domain of (f/g)(x) = All real numbers except x = 0
3. (f/g)(81) = 108
f (x) = x + 3
g (x) = 4x2
Find g(f(–8))
g(f(–8)) = 100
Find the inverse of the function below:
f(x) = –½x + 10
f –1(x)= –2x + 20
f (x) = 2x2 + 11x
g (x) = –3x2 – 7x + 4
Find:
1. (f + g)(x)
2. The domain of (f + g)(x)
3. (f + g)(2)
1. (f + g)(x) = –x2 + 4x + 4
2. Domain of (f + g)(x) = All real numbers
3. (f + g)(2) = 8
f (x) = 3x2
g (x) = x¼
Find:
1. (fg)(x)
2. The domain of (fg)(x)
3. (fg)(16)
1. (fg)(x) = 3x9/4
2. Domain of (fg)(x) = x ≥ 0
3. (fg)(16) = 1,536
f (x) = 15x
g (x) = 3x¾
Find:
1. (f/g)(x)
2. The domain of (f/g)(x)
3. (f/g)(625)
1. (f/g)(x) = 5x¼
2. Domain of (f/g)(x) = All real numbers except x = 0
3. (f/g)(625) = 25
g (x) = 4x2
h (x) = √(x – 7)
Find h(g(2))
h(g(2)) = 3
Find the inverse of the function below:
f(x) = x3 – 12
f –1(x)= ∛(x + 12)
f (x) = 5∜(x)
g (x) = –19∜(x)
Find:
1. (f – g)(x)
2. The domain of (f – g)(x)
3. (f – g)(16)
1. (f – g)(x) = 24∜(x)
2. Domain of (f – g)(x) = x ≥ 0
3. (f – g)(16) = 48
f (x) = x3
g (x) = 2∛(x )
Find:
1. (fg)(x)
2. The domain of (fg)(x)
3. (fg)(8)
1. (fg)(x) = 2x10/3
2. Domain of (fg)(x) = All real numbers
3. (fg)(8) = 2,048
f (x) = 3√(x)7
g (x) = x3
Find:
1. (f/g)(x)
2. The domain of (f/g)(x)
3. (f/g)(144)
1. (f/g)(x) = 3x½
2. Domain of (f/g)(x) = All real numbers except x = 0
3. (f/g)(144) = 36
f (x) = 2x – 5
h (x) = 3x + 4
Find:
1. h(f(x))
2. The domain of h(f(x))
1. h(f(x)) = 6x – 11
2. Domain of h(f(x)) = All real numbers
Find the inverse of the function below:
f(x) = x2 + 8, x ≥ 0
f –1(x)= √(x – 8)
f (x) = 9x3 + 3x2 – 2x + 4
g (x) = 7x3 – 2x2 – 7x – 1
Find:
1. (f – g)(x)
2. The domain of (f – g)(x)
3. (f – g)(–2)
1. (f – g)(x) = 2x2 + 5x2 + 5x + 5
2. Domain of (f + g)(x) = All real numbers
3. (f + g)(2) = –1
f (x) = 7x3/2
g (x) = –3x⅓
Find:
1. (fg)(x)
2. The domain of (fg)(x)
3. (fg)(64)
1. (fg)(x) = –21x11/6
2. Domain of (fg)(x) = x ≥ 0
3. (fg)(64) = –43,008
f (x) = 5x3/2
g (x) = –10x⅓
Find:
1. (f/g)(x)
2. The domain of (f/g)(x)
3. (f/g)(64)
1. (f/g)(x) = –½ x7/6
2. Domain of (f/g)(x) = All real numbers except x = 0
3. (f/g)(64) = –64
g (x) = x–2
h (x) = 3x + 4
Find:
1. g(h(x))
2. The domain of g(h(x))
1. g(h(x)) = 1/(3x + 4)2
2. Domain of g(h(x)) = All real numbers except x = –4/3
Find the inverse of the function below:
f(x) = 3√(x + 5)
f –1(x) = 1/9 x2 – 5, x ≥ 0