a$.$ Let g$($x$)=5$x $+3$ and h$($x$)=$ x$^3.$ Consider the composite function f$($x$)=$ g$($h$($x$)).$ Find f$^-1$ directly and then express the inverse of f in terms of g$^-1$ and h$^-1.$

b$.$ Let g$($x$)=$ x$^2+3$ and h$($x$)=$ sq$.$rt$($x$).$ Consider the composite function f$($x$)=$ g$($h$($x$)).$ Find f$^-1$ directly and then express it in terms of g$^-1$ and h$^-1.$

c$.$ Explain why if g and h are one$-$to$-$one, the inverse of f$($x$)=$ g$($h$($x$))$ exists.