Not substituting properly into function expressions H
"The Substitution Slip"
The Mistake in Action
Given $f(x) = x^2 + 1$. Find $f(x + 2)$.
Wrong: $f(x + 2) = x^2 + 1 + 2 = x^2 + 3$
Why It Happens
Students add 2 to the expression instead of replacing every $x$ with $(x + 2)$.
The Fix
$f(x + 2)$ means replace every $x$ in the formula with $(x + 2)$.
$f(x) = x^2 + 1$
$f(x + 2) = (x + 2)^2 + 1$ $= x^2 + 4x + 4 + 1$ $= x^2 + 4x + 5$
The pattern: $f(\text{something})$ means put that "something" wherever you see $x$ in the formula.
Spot the Mistake
Can you identify where this student went wrong?
$f(x) = x^2 + 1$, find $f(x+2)$
$f(x + 2) = x^2 + 1 + 2 = x^2 + 3$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: