Questions: The formula F(C) = (9/5) C + 32 calculates the temperature in degrees Fahrenheit, given a temperature in degrees Celsius. You can find an equation for the temperature in degrees Celsius for a given temperature in degrees Fahrenheit by finding the function's (F-32) => inverse X. The inverse of F(C) = (9/5) C + 32 is C(F) = square F - square

The formula F(C) = (9/5) C + 32 calculates the temperature in degrees Fahrenheit, given a temperature in degrees Celsius.

You can find an equation for the temperature in degrees Celsius for a given temperature in degrees Fahrenheit by finding the function's (F-32) => inverse X.

The inverse of F(C) = (9/5) C + 32 is
C(F) = square F - square

Transcript text: The formula $F(C)=\frac{9}{5} C+32$ calculates the temperature in degrees Fahrenheit, given a temperature in degrees Celsius. You can find an equation for the temperature in degrees Celsius for a given temperature in degrees Fahrenheit by finding the function's $(F-32) \Rightarrow$ inverse $\mathbf{X}$. COMPLETE The inverse of $F(C)=\frac{9}{5} C+32$ is \[ C(F)=\square F-\square \]

Solution

Solution Steps

Step 1: Express the original function

The original function is given as: \[ F(C) = \frac{9}{5}C + 32 \] This function converts a temperature $ C $ in degrees Celsius to a temperature $ F $ in degrees Fahrenheit.

Step 2: Solve for $ C $ in terms of $ F $

To find the inverse function $ C(F) $, we solve the equation for $ C $: \[ F = \frac{9}{5}C + 32 \] Subtract 32 from both sides: \[ F - 32 = \frac{9}{5}C \] Multiply both sides by $ \frac{5}{9} $ to isolate $ C $: \[ C = \frac{5}{9}(F - 32) \]

Step 3: Write the inverse function

The inverse function $ C(F) $ is: \[ C(F) = \frac{5}{9}F - \frac{160}{9} \] This function converts a temperature $ F $ in degrees Fahrenheit to a temperature $ C $ in degrees Celsius.