2024 SJI P2 Q6

A function \(\mathrm f\) is defined as \(\mathrm f(x)=3^x-\dfrac1{3^x}\), \(x\in\mathbb R\).

1. Determine if \(\mathrm f\) is an even or odd function, or neither.[3]

Consider a one-one function \(\mathrm g\) such that \(\mathrm g(0)=1\) and \(\mathrm g'(0)=2\).

2. Find the value of \((\mathrm f\circ\mathrm g)(0)\).[2]
3. Find the value of \((\mathrm f\circ\mathrm g)'(0)\).[3]
4. Find the value of \(x\) such that \((\mathrm g^{-1}\circ\mathrm f)(x)=0\).[3]