Common Algebra Mistakes Function Notation Some problems provide the opportunity for more than one mistake. The Goal Evaluate f(x+h) for the function: The Mistakes Find the mistakes: 1. (Roll the mouse over the math to see a hint in red) 2. (Roll the mouse over the math to see a hint in red) A Correct Solution (Roll the mouse over the area above to see the corrections in blue) Explanations In the first mistake f(x+h) is computed to be f(x)+h. There are very few functions f(x) for which the equation f(x+h) = f(x) + h is true (it is true if y = f(x) is a straight line with slope 1). The mistake in thinking that f(x+h) = f(x) + h is true in general comes from not properly understanding function notation.In f(x) the x is a placeholder. To evaluate f(x+h) we must put x+h in for that placeholder precisely where x appears in f(x) - no more and no less. In the second example the +h is again in the wrong place. Follow the sequence of examples: The function f(x): Whatever we replace x with replaces x in the formula (even something silly like #): Replace x with 0.5 to find f(0.5): Note that 0.5 can be written as 0.4+0.1: Following the pattern we can find f(0.4+h): And f(x+h) is a matter of replacing the 0.4 by x: Home Page | Common Algebra Mistakes | Privacy Policy