Question

The function c(f) = 5/9 (f-32) allows you to convert degrees to Fahrenheit to degrees Celsius. Find the inverse of the function so that you can convert degrees Celsius back to degrees Fahrenheit

Answer 1

For this case we have the following function:

`c (f) = \frac {5} {9} (f-32)`

We must find the inverse function. For this we follow the steps below:

Replace c (f) with y:

`y = \frac {5} {9} (f-32)`

We exchange variables:

`\frac {5} {9} (y-32) = f`f = \frac {5} {9} (y-32)

We solve for "y":

`\frac {5} {9} (y-32) = f`

We multiply by
`\frac {9} {5}`on both sides of the equation:

`y-32 = \frac {9} {5} f`

We add 32 to both sides of the equation:

`y = \frac {9} {5} f + 32`

We change y by
`c^( -1) (f):`

`c^(-1) (f) = \frac {9} {5} f + 32`

Answer:

`c^(-1) (f) = \frac {9} {5} f + 32`

Answer 2

`f(c)=(9)/(5)c+32`

Explanation:

Given function that is used to convert degrees to Fahrenheit to degrees Celsius,

`c(f)=(5)/(9)(f-32)`

Let y represents the output value of the function and x represents the input value,

`y=(5)/(9)(x-32)`

Switch x and y,

`x=(5)/(9)(y-32)`

Isolate y,

`9x=5(y-32)`

`(9)/(5)x=y-32`

`\implies y = (9)/(5)x+32`

`\implies f(c)=(9)/(5)c+32`

Which is the required function.