### About Operations on Functions:

When we work with functions, we use a very specific notation to ask for the functions value given a certain input for the independent variable. Additionally, we will be looking at two new scenarios: adding/subtracting two polynomial functions and multiplying/dividing two polynomial functions.

Test Objectives

- Demonstrate the ability to use function notation
- Demonstrate the ability to add/subtract polynomial functions
- Demonstrate the ability to multiply/divide polynomial functions

#1:

Instructions: Perform each indicated operation.

a) $$g(x) = -5x^3 - 7x + 1$$ find: $$g(0),~g(-1), ~g(-3)$$

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#2:

Instructions: Perform each indicated operation.

a) $$f(x) = 7x^3-9x+4$$ $$h(x) = 12x^3 + 6x$$ $$g(x) = -19x^3 + 2x^2 - 5$$ find: $$(f + h + g)(x)$$ $$(f + h + g)(-2)$$

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#3:

Instructions: Perform each indicated operation.

a) $$f(x) = -5x^3-13x^2+2x-12$$ $$g(x) = 5x^3 - x^2 - 13x$$ $$h(x) = -9x^3 - 10x^2 + x + 10$$ find: $$(f - g - h)(x)$$ $$(f - g - h)(-1)$$

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#4:

Instructions: Perform each indicated operation.

a) $$f(x) = 3x$$ $$g(x) = 6x - 6$$ $$h(x) = 7x + 4$$ find: $$(fgh)(x)$$ $$(fgh)(-1)$$

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#5:

Instructions: Perform each indicated operation.

a) $$f(x) = 7x^3 - 24x^2 + 16x - 21$$ $$g(x) = x - 3$$ find: $$\frac{f}{g}(x)$$ $$\frac{f}{g}(-5)$$

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Written Solutions:

#1:

Solutions:

a) $$g(0) = 1$$ $$g(-1) = 13$$ $$g(-3) = 157$$

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#2:

Solutions:

a) $$(f + g + h)(x) = 2x^2 - 3x - 1$$ $$(f + g + h)(-2) = 13$$

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#3:

Solutions:

a) $$(f - g - h)(x) = -x^3 - 2x^2 + 14x - 22$$ $$(f - g - h)(-1) = -37$$ $$(f - g - h)(x) = $$$$-x^3 - 2x^2 + 14x - 22$$ $$(f - g - h)(-1) = -37$$

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#4:

Solutions:

a) $$(fgh)(x) = 126x^3 - 54x^2 - 72x$$ $$(fgh)(-1) = -108$$

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#5:

Solutions:

a) $$\frac{f}{g}(x) = 7x^2 - 3x + 7$$ $$\frac{f}{g}(-5) = 197$$