Contents of Compound Definitions

Compound Definitions

If g and h are previously defined functions (other than piecewise-defined functions), then the following equations are examples of legitimate definitions:

f (x) = 2g(x)
f (x) = g(x) + h(x)
f (x) = g(x)h(x)
f (x) = g(h(x))
f (x) = $\left(\vphantom{ g\circ h}\right.$ goh $\left.\vphantom{ g\circ h}\right)$ (x)

Once you have defined both g(x) and f (x) = 2g(x), then changing the definition of g(x) will redefine f (x).

Note The algebra of functions includes objects such as f + g,f - g, fog, fg, and f^-1. For the value of f + g at x, write f (x) + g(x); for the value of the composition of two defined functions f and g, write f (g(x)) or $\left(\vphantom{ f\circ g}\right.$ fog $\left.\vphantom{ f\circ g}\right)$ $\left(\vphantom{ x}\right.$ x $\left.\vphantom{ x}\right)$ ; and for the value of the product of two defined functions, write f (x)g(x). You can obtain the inverse (or inverse relation) for some functions f (x) by applying Solve + Exact to the equation f (y) = x and specifying y as the Variable to Solve for.