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

Answer:

$f(c)=\frac{9}{5}c+32$

Step-by-step explanation:

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

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

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

$y=\frac{5}{9}(x-32)$

Switch x and y,

$x=\frac{5}{9}(y-32)$

Isolate y,

$9x=5(y-32)$

$\frac{9}{5}x=y-32$

$\implies y = \frac{9}{5}x+32$

$\implies f(c)=\frac{9}{5}c+32$

Which is the required function.