Answer
(a) $f(n)=1.5n+16$
(b) $f^{-1}(n)=\frac{2n-32}{3}$
$f^{-1}(n)$ represents number of toppings for given $n$ amount of money.
(c) The pizza has $6$ toppings.
Work Step by Step
(a) So, we have function $f$ representing the price of pizza and $n$ (variable) for amount of toppings. In addition we know that for any amount of topping we have unchangeable $16\$$ (constant) and $1.5\$$ for each topping. According to the information provided, we can simply write:
$f(n)=1.5n+16$
(b) To find the inverse of the function $f$ we will follow the next steps:
First write the function in terms of $y$ and $n$ (In our case $n$ stands for the $x$ we have in general cases):
$y=1.5n+16$
Then replace $y$ by $n$ and vice versa:
$n=1.5y+16$
And at last solve for $y$:
$1.5y=n-16$
$y=\frac{n-16}{1.5}$
$y=\frac{2(n-16)}{3}$
$y=\frac{2n-32}{3}$
$f^{-1}(n)=\frac{2n-32}{3}$
$f^{-1}(n)$ represents number of toppings for given $n$ amount of money. Which is also clear, due to the definition of an inverse function; we replace $y$ (amount of money) by $n$ (number of toppings)
(c) If pizza costs $\$25$, it means $f(n)=25$
$25=1.5n+16$
$1.5n=9$
$n=6$
It has $6$ toppings.
