Review question

# For which $x$-values does a function equal its inverse? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6735

## Suggestion

A function $f$ is defined by $f:x\rightarrow \dfrac{1}{x+1}$. Write down in similar form expressions for $f^{-1}...$

How can we find the inverse function? What happens if we make $x$ the subject of $y=f(x)$?

… and $ff$.

Would it help to view the composite function $ff(x)$ as $f(f(x))$?

It is required to find the values of $x$ for which $(i)$ $f=f^{-1}$, $(ii)$ $f=ff$.

Show that, in each case, the values of $x$ are given by the equation $x^2+x-1=0.$

From the above, we should now know $f(x)$, $f^{-1}(x)$ and $ff(x)$. Can we form equations using these?