Question

Please help me with this for 20 points

Answer 1

`\large a)\ f(x)=(5)/(9)(x-32)\\\\b)\ f^(-1)(x)=(9)/(5)x+32\\\\9^oC=48.2^oF`

Explanation:

`C=(5)/(9)(F-32)\\\\a)\ f(x)=(5)/(9)(x-32)\\\\b)\ C=(5)/(9)(F-32)\\\\\text{solve for F}\\\\(5)/(9)(F-32)=C\qquad\text{multiply both sides by 9}\\\\5(F-32)=9C\qquad\text{divide both sides by 5}\\\\F-32=(9)/(5)C\qquad\text{add 32 to both sides}\\\\F=(9)/(5)C+32\\\\f^(-1)(x)=(9)/(5)x+32`

`c)\ \text{Put}\ x=9\ \text{to}\ f^(-1)(x):\\\\f^(-1)(9)=(9)/(5)(9)+32=(81)/(5)+32=16.2+32=48.2\\\\9^oC=48.2^oF`