Answer: 0.67857
Explanation:
a ) Given the equation we simply group terms and solve n for c =4.75:
[tex]c = 4n+3n\\c = n(4+3)\\c/7 =n=>4.75/7 = 0.678\\\\[/tex]
b) We first check if the function is invertible (let n1 and n2 be any values for the function c = 4n+3n) So we have to prove ([tex]f(n_{1}) = f(n_{2})[/tex] => [tex]n_{1} = n_{2}[/tex])
so we have[tex]f(n_{1})= 7n_{1}\\f(n_{2}) = 7n_{2}\\ Â ( f(n_{1}) =f(n_{2}) ) =(7n_{1}=7n_{2}) = (n_{1}=n_{2})[/tex]
finally [tex]n_{1} = n_{2}[/tex]. This is a check you always do to find if a function is invertible (it has to be injective).
Now solving the problem we just replace c with n and n with c:
[tex]n = 4c + 3c = c(4+3) = 7c => n/7 = c[/tex]
where n = 4.75
finally:
[tex]c = 4.75/7 = 0.67857[/tex]
that is the number of games you need.
