EVALUATING WITH FUNCTION OPERATIONS WORKSHEET

Problem 1 :

Let f(x) = 4x - 1 and g(x) = 2x² + 3. Perform each function operation and then find the domain.

1. f(x) + g(x)

2. f(x) - g(x)

4. g(x) - f(x)

5. f(x) · g(x)

Solution:

1.

f(x) + g(x) :

= 4x - 1 + 2x² + 3

= 2x² + 4x + 2

Domain : All real numbers

2. 

f(x) - g(x) :

= 4x - 1 - 2x² - 3

= -2x² + 4x - 24

Domain : All real numbers

3. 

Domain : All real numbers

4. 

g(x) - f(x) :

= 2x² + 3 - 4x + 1

= 2x² - 4x + 4

Domain : All real numbers

5.

f(x) · g(x) :

= (4x - 1) · (2x² + 3)

= 8x³ + 12x - 2x² - 3

Domain : All real numbers

6.

4x - 1 ≠ 0

x ≠ 1/4

Domain : (-∞, 1/4) ∪ (1/4, +∞)

Problem 2 :

Let f(x) = -3x + 2, g(x) = x/5, h(x) = -2x² + 9, and j(x) = 5 - x. Find each value or expression.

1. (f ∘ j)(3)

2. (j ∘ h)(-1)

3. (h ∘ g)(-5)

4. (g ∘ f)(a)

5. f(x) + j(x)

6. f(x) - h(x)

7. (g ∘ f)(-5)

8. (f ∘ g)(-2)

9. 3f(x) + 5g(x)

10. g(f(2))

11. g(f(x))

12. f(g(1))

Solution:

1.

(f ∘ j)(3) = f(j(3))

= f(5 - 3)

= f(2)

= -3(2) + 2

= -4

2. 

(j ∘ h)(-1) = j(h(-1))

= j(-2(-1)² + 9)

= j(7)

= 5 - 7

= -2

3.

(h ∘ g)(-5) = h(g(-5))

= h(-5/5)

= h(-1)

= -2(-1)² + 9

= 7

4. 

(g ∘ f)(a) = g(f(a))

= g(-3a + 2)

5. 

f(x) + j(x) = -3x + 2 + 5 - x

= -4x + 7

6. 

f(x) - h(x) = -3x + 2 + 2x² - 9

= 2x² - 3x - 7

7.

(g ∘ f)(-5) = g(f(-5))

= g(-3(-5) + 2)

= g(17)

= 17/5

8. 

(f ∘ g)(-2) = f(g(-2))

= f(-2/5)

= -3(-2/5) + 2

= 6/5+2

= 16/5

9.

3f(x) + 5g(x) = 3(-3x + 2) + 5(x/5)

= -9x + 6 + x

= -8x + 6

10.

g(f(2)) = g(-3(2) + 2)

= g(-4)

= -4/5

11.

g(f(x)) = g(-3x + 2)

12.

f(g(1)) = f(1/5)

= -3(1/5) + 2

= -3/5 + 2

= 7/5