Composite and Inverse Functions (VCE SSCE Mathematical Methods): Quizzes

Apply $f$ first, then apply $g$

Range of $f$ must be in domain of $g$

$f(x) = x^2$ and $g(x) = e^x$

It must be one-to-one

Domain of $f^{-1}$ equals range of $f$

Whenever $a > b$, we have $f(a) > f(b)$

Whenever $a > b$, we have $f(a) < f(b)$

Yes, they are always one-to-one

$f^{-1}$ is strictly increasing

$g^{-1}(x) = \frac{1}{x^2}$