Evaluate: {\text{begin}array l-x+3y=-15 } 3x+3y=21\text{end}array .

Expression: $f\left( x \right)={2.1}^{x}$

Substitute $y$ for $f\left( x \right)$

$y={2.1}^{x}$

Interchange $x$ and $y$

$x={2.1}^{y}$

Swap the sides of the equation

${2.1}^{y}=x$

Convert the decimal into a fraction

${\left( \frac{ 21 }{ 10 } \right)}^{y}=x$

Take the logarithm of both sides of the equation

$y=\log_{ \frac{ 21 }{ 10 } }({ x })$

Substitute $f^{-1}\left( x \right)$ for $y$

$f^{-1}\left( x \right)=\log_{ \frac{ 21 }{ 10 } }({ x })$