Combining Functions

f(x)

sin(x)

cos(x)

2

x

1

2

x

+1

2

x

+1

2

(1-x)

x

3

x

g(x)

sin(x)

cos(x)

2

x

1

2

x

+1

2

x

+1

2

(1-x)

x

3

x

combination

f(x)+g(x)

f(x)-g(x)

g(x)-f(x)

f(x)g(x)

f(x)/g(x)

g(x)/f(x)

f(g(x))

g(f(x))

zoom

Functions can be combined through addition, subtraction, and other operations in the same ways that numbers can. They can also be combined by composition, as shown by the last two choices in the combination setter. Arithmetic combinations of a periodic and a non-periodic function are not periodic, but compositions might be periodic, like

cos(x)

.