Function Notation

Function Notation

If a relation is a function sometimes we use f(x) (read f of x) instead of y.
For example, instead of writing y = 5x2 - 3x + 7 , we may write f(x) = 5x2 - 3x + 7. (This does not mean f times x, it is merely a notation.) This notation indicates that numbers or expressions need to be plugged in for the variable.

Suppose we want to evaluate the function f(x), defined above, at x = 3. We would say find f(3) ("f of 3"). Again this does not mean f times 3, it is only a notation. The notation f(3) tells us to plug in 3 for x in the function f. In function notation, we replace the variable with whatever is inside the parenthesis.

Sometimes we will deal with more than one function, so we name them to differentiate between them. We may use any letter to name our function. Commonly used letters are f, g, and h, but others may be used.

Given the above two functions f(x), "f of x", and g(x), "g of x", we will evaluate each of the following.

1. f(5)

This tells us to replace the x in f(x) with 5.

2. g(x + h)

This tells us to replace the x in g(x) with (x + h)

3. g( 1/2 )

This tells us to replace the x in g(x) with 1/2;

Practice problems


Given the above two equations, evaluate each of the following?

1. f(3x)

2. h(2)

3. f(x + h)

4. h(-3)

Solutions


Solutions

1. f(3x)

This tells us to replace x in f with 3x.

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2. h(2)

This tells us to replace x in h with 2.

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3. f(x + h)

This tells us to replace x in f with x + h.

Remember we must foil (x + h)2 and distribute the negative to both x and the h.

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4. h(-3)

This tells us to replace x in h with -3

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Back to the definition of functions