High School

The function [tex]F(C) = \frac{9}{5}C + 32[/tex] converts a temperature from degrees Celsius [tex]C[/tex] to degrees Fahrenheit [tex]F[/tex].

(a) Express the temperature in degrees Celsius [tex]C[/tex] as a function of the temperature in degrees Fahrenheit [tex]F[/tex].

(b) Verify that [tex]C = C(F)[/tex] is the inverse of [tex]F = F(C)[/tex] by showing that [tex]C(F(C)) = C[/tex] and [tex]F(C(F)) = F[/tex].

(c) What is the temperature in degrees Celsius if it is 70 degrees Fahrenheit?

Answer :

(a) To express the temperature in degrees Celsius C as a function of the temperature in degrees Fahrenheit F, we need to rearrange the equation F(C) = (9/5)C + 32 to solve for C.

F(C) = (9/5)C + 32

Subtract 32 from both sides:

F(C) - 32 = (9/5)C

Multiply both sides by (5/9):

(5/9)(F(C) - 32) = C

So, the function to convert temperature from Fahrenheit to Celsius is:

C(F) = (5/9)(F - 32)

(b) To verify that C = C(F) is the inverse of F = F(C), we substitute C(F) into F(C) and F(C(F)) into C(F) and check if we get the original values:

F(C(F)) = F[(5/9)(F - 32)]

= (9/5)[(5/9)(F - 32)] + 32

= F - 32 + 32

= F

C(F(C)) = C[(9/5)C + 32]

= (5/9)[(9/5)C + 32 - 32]

= C

Since both C(F(C)) and F(C(F)) result in the original values C and F, we can conclude that C = C(F) is the inverse of F = F(C).

(c) If it is 70 degrees Fahrenheit, we can use the function C(F) = (5/9)(F - 32) to find the temperature in degrees Celsius:

C(70) = (5/9)(70 - 32)

= (5/9)(38)

≈ 21.11 degrees Celsius

Therefore, if it is 70 degrees Fahrenheit, the temperature in degrees Celsius would be approximately 21.11 degrees Celsius.

Learn more about Fahrenheit here

https://brainly.com/question/30395861

#SPJ11