Substituting Expressions

In addition to substituting numbers and other variables into a function, you can substitute entire expressions such as a+b, x² or 3x into a function

To do this, you replace all instances of x with the expression, then simplify. See the examples using f(x) = 3x + 2 below for a demonstration.

Example 1: If f(x) = 3x + 2 then:

1. f(a) = 3a + 2
2. f(a+b) = 3•(a+b) + 2
               = 3a + 3b + 2
3. f(x²) = 3•(x²) + 2
           = 3x² + 2
4. f(3x) = 3•(3x) + 2
             = 9x + 2

Example 2: If f(x) = x² - 3x then:

1. f(a) = (a)² - 3•(a) = a² - 3a
2. f(a+b) = (a+b)² - 3•(a+b)
               = a² + 2ab +b² - 3a -3b
3. f(x²) = (x²)² - 3•(x²)
           = 3x⁴ + 2
4. f(3x) = (3x)²- 3•(3x)
             = 9x² - 9x

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