# EVALUATING WITH FUNCTION OPERATIONS WORKSHEET

To evaluate function operations, we should know how to add, subtract, multiply and divide functions.

Adding and subtracting functions is like combining like terms.

Multiplying functions :

To multiply two functions, we have to use distributive property and using the properties of exponents we can multiply the functions.

Dividing functions :

To divide two functions and if they both are rational functions, we have to keep the first function as it is, change the division sign as multiplication and write the reciprocal of the second function.

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

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