If f(x) = {(3,5), (2,4), (1,7)}
g(x) = √x-3
h(x) = {(3,2), (4,3), (1,6)}
k(x) = x^2 + 5
determine the following:
1. (f+h)(1)
2. (k-g)(5)
3. (foh)(3)
4. (gok)(7)
5. f^-1(x)
6. k^-1(x)
7. 1/f(x)
8. (kg)(x)
g(x) = √x-3
h(x) = {(3,2), (4,3), (1,6)}
k(x) = x^2 + 5
determine the following:
1. (f+h)(1)
2. (k-g)(5)
3. (foh)(3)
4. (gok)(7)
5. f^-1(x)
6. k^-1(x)
7. 1/f(x)
8. (kg)(x)
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1. (f+h)(1) = f(1) + h(1) = 7 + 6 = 13
2. (k-g)(5) = k(5) - g(5) = 30 - (√5 - 3) = 33 - √5
{ unless you meant g(x) = √(x - 3) }
3. (f ○ h)(3) = f( h(3)) = f( 2) = 4
4. (g ○ k)(7) = g( k(7)) = g( 54) = 3√6 - 3
5. f^-1(x) = { (5,3), (4,2), (7,1) }
6. k^-1(x) = this has inverse only for x ≥ 0, k^-1(x) = √(x - 5)
7. 1/f(x) = { (3, 1/5), (2, 1/4), (1, 1/7) }
8. (kg)(x) = again, if you meant √(x - 3) you should'a used the ()
∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ = (√x - 3)² + 5 = x - 6√x + 9 + 5 = x - 6√x + 14
2. (k-g)(5) = k(5) - g(5) = 30 - (√5 - 3) = 33 - √5
{ unless you meant g(x) = √(x - 3) }
3. (f ○ h)(3) = f( h(3)) = f( 2) = 4
4. (g ○ k)(7) = g( k(7)) = g( 54) = 3√6 - 3
5. f^-1(x) = { (5,3), (4,2), (7,1) }
6. k^-1(x) = this has inverse only for x ≥ 0, k^-1(x) = √(x - 5)
7. 1/f(x) = { (3, 1/5), (2, 1/4), (1, 1/7) }
8. (kg)(x) = again, if you meant √(x - 3) you should'a used the ()
∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ = (√x - 3)² + 5 = x - 6√x + 9 + 5 = x - 6√x + 14