Foolish invertible g(x) !!

$First\quad thing\quad that\quad strike\quad in\quad mind\quad to\quad do\quad question\quad is\\ by\quad using\quad Leibnitz\quad Theoram...But\quad Plz\quad avoid\quad it\quad here\\ Let's\quad do\quad some\quad diffrent....\quad :\\ Note\quad That\quad :\quad \\ \int _{ a }^{ b }{ 1.dx } =b-a\\ so\quad according\quad to\quad question\quad \\ \Longrightarrow \quad { e }^{ ln(f(sin^{ 2 }{ t) }cos^{ 2 }{ t } }=1\\ \Longrightarrow \quad f(sin^{ 2 }{ t) }cos^{ 2 }{ t }=1\\ \Longrightarrow \quad f(sin^{ 2 }{ t) }=\frac { 1 }{ cos^{ 2 }{ t } } =\frac { 1 }{ 1-sin^{ 2 }t } \\ \\ \Longrightarrow f\left( x \right) =\frac { 1 }{ 1-x } \quad \forall \quad x\quad \in \quad \left[ -1,1 \right] \\ \\ \longrightarrow \quad f(1/2).f(1/3)=3\quad Ans.$ .