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 d…

Question

asked May 17, 2020 158k views

2 Answers

Andrew Marsh · Answer 1 · 2020-05-18T01:00:08+0000

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:

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

Darkbluesun · Answer 2 · 2020-05-21T02:16:07+0000

Answer:

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.