Question

The function given by f (x) = 9/5 x + 32 converts x degrees Celsius to an equivalent temperature in degrees Fahrenheit.
(a) Is f a one-to-one function? Why or why not?
(b) Find f -1(x) and interpret what it calculates

Answer 1

a) you are dealing with a linear function (a straight line graph)
Unless the line is vertical or horizontal, all linear functions are 1 to 1

b) f = (9/5) x + 32
the inverse is
x = (9/5)f + 32
x - 32 = (9/5)f
(5(x-32))/9 = f

f = (5/9)( x - 32)

or in your notation
f^-1 (x) = (5/9)(x - 32)

your first function converts a temperature in Celcius to Fahrenheit, while the second converts from F° to C°