Operations with functions

Operations with Functions

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f(x)=2x-4

g(x)=-3x+5

(f+g)(x)=(2x-4)+(-3x+5)

(f+g)(x)=-x+1

Example

When you see the notation

(f+g)(x), this means to add f(x) to g(x). You are taking the two functions and combining like terms.

Notes

Adding Functions

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f(x)=2x-4

g(x)=-3x+5

(f-g)(x)=(2x-4)-(-3x+5)

(f-g)(x)=5x-9

Example

When you see the notation

(f-g)(x), this means to subtract g(x) from f(x). You are taking the two functions and combining like terms.

Notes

Subtracting Functions

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f(x)=2x-4

g(x)=-3x+5

(f⋅g)(x)=(2x-4)(-3x+5)

(f⋅g)(x)=-6x²+22x-20

Example

When you see the notation

(f⋅g)(x), this means to multiply f(x) and g(x). You will need to use the distributive property or FOIL to get your final answer.

Notes

Multplying Functions

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f(x)=2x-4

g(x)=-3x+5

(f/g)(x)=(2x-4)/(-3x+5)

There is no way to simplify further. Leave as fraction.

Example

When you see the notation

(f/g)(x), this means to divide f(x) by g(x). Most times you will just be rewriting the function as a fraction. Sometimes you may be able to simplify.

Notes

Dividing Functions

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