A trader has a mixture of $5c$ and $10c$ coins. He has $50$ coins in all, with a total value of $\$4.20$. How many of each coin does he have?
 

$f$ and $g$ are the functions $f:x\to x-5$ and $g:x\to 5-x$.

State whether the following statement is true or false.

$f^{-1}=g$

$f$ and $g$ are the functions $f:x\to x-5$ and $g:x\to 5-x$.

State whether the following statement is true or false.

$g^{-1}: x\to 5-x$

$f$ and $g$ are the functions $f:x\to x-5$ and $g:x\to 5-x$.

State whether the following statement is true or false.

$fg: x\to -x$

$f$ and $g$ are the functions $f:x\to x-5$ and $g:x\to 5-x$.

State whether the following statement is true or false.

$fg=gf$

$f\left(x\right)=3x^2-3x-4$ and $g\left(x\right)=4-3x$.

 Solve the equation $f\left(x\right)=-3$.