Defining Generic Functions

You can use Define + New Definition to declare an expression of the form f (x) to be a function without specifying any of the function values or behavior. Thus you can use the function name as input when defining other functions or performing various operations on the function.

$\blacktriangleright$ Define + New Definition

f (x)

g(x) = x2 - 3x

$\blacktriangleright$ Evaluate

f (g(x)) = f$\left(\vphantom{ x^{2}-3x}\right.$x2 - 3x$\left.\vphantom{ x^{2}-3x}\right)$


g(f (x)) = f2$\left(\vphantom{ x}\right.$x$\left.\vphantom{ x}\right)$ -3f$\left(\vphantom{ x}\right.$x$\left.\vphantom{ x}\right)$