Linear Functions (Grade 12 NSC Matric Mathematics): Flashcards

Role of inverse function

Reverses the effect of the original function

Meaning of $f^{-1}(x)$ notation

Inverse function, NOT $\frac{1}{f(x)}$

3 steps to find inverse function

1. Swap x & y 2. Make y subject 3. Function notation

Inverse of $y = ax + q$

$y = \frac{1}{a}x - \frac{q}{a}$

Condition for function to have inverse

Must be one-to-one (injective)

Domain & range relationship for inverses

They swap: domain of $f$ = range of $f^{-1}$

Intercept coordinates for $f$ and $f^{-1}$

Swap: $(a,b)$ on $f$ becomes $(b,a)$ on $f^{-1}$

Graph of $f^{-1}$ relative to $f$

Reflection of $f$ about line $y = x$

Point $(a,b)$ on $f(x)$ maps to what on $f^{-1}(x)$

Point $(b,a)$

Verification property of inverse functions

$f(f^{-1}(x)) = x$ and $f^{-1}(f(x)) = x$