Part $1$

The function

f left parenthesis x right parenthesis equals StartFraction $9$ x plus $5$ Over x minus $3$ EndFractionf$($x$)=9$x$+5$x$3$

is$$ one$-$to$-$one.

a$.$ Find an equation for

f Superscript negative $1$ Baseline left parenthesis x right parenthesisf$1($x$),$

the inverse function.

b$.$ Verify that your equation is correct by showing that

f left parenthesis f Superscript negative $1$ Baseline left parenthesis x right parenthesis right parenthesisff$1($x$)$equals$=$x

and

f Superscript negative $1$ Baseline left parenthesis f left parenthesis x right parenthesis right parenthesisf$1($f$($x$))$equals$=$x$.$