Operations Involving Functions (Leaving Cert Mathematics): Flashcards

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Operations Involving Functions
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Three ways to write same function

f(x)=...f(x) = ..., f:x→...f: x → ..., y=...y = ...

Format: f(x)=3x−2f(x) = 3x - 2

Function notation

Format: f:x→3x−2f: x → 3x - 2

Mapping notation

Format: y=3x−2y = 3x - 2

Equation form

What f(3)f(3) represents

Output value when input is 3

Why use different letters (g(x)g(x), h(x)h(x))?

To distinguish between multiple functions

Composite function definition

One function applied to result of another

Meaning of gfgf

gg after ff

Alternative notation for gfgf

g∘fg \circ f

Does fg(x)=gf(x)fg(x) = gf(x)?

No, order matters

For gf(x)gf(x), which function to apply first?

Apply ff first, then gg to result

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