The equation C = 5 9 F − 160 9 gives the relation between temperature readings in Celsius and Fahrenheit. (a) Is C a function of F? Yes, C is a function of F. No, C is a not a function of F.

(b) What is the mathematical domain of this function? (Enter your answer using interval notation. If C is not a function of F, enter DNE.)

(c) If we consider this equation as relating temperatures of water in its liquid state, what are the domain and range? (Enter your answers using interval notation. If C is not a function of F, enter DNE.) domain range

(d) What is C when F = 71°? (Round your answer to two decimal places. If C is not a function of F, enter DNE.) C(71) = °C

Step-by-step explanation:

The question is wrong. The correct equation is :

We know that the equation gives the relation  between temperature readings in Celsius and Fahrenheit.

Therefore, giving that we know the value in Fahrenheit ''F'' we can find the reading in Celsius ''C''. This define a function C(F) that depends of the variable ''F''.

So for the incise (a) we answer Yes, C is a function of F.

For (b) we need to find the mathematical domain of this function. Giving that we haven't got any mathematical restriction, the mathematical domain of the function are all real numbers.

Dom (C) = ( - ∞ , + ∞)

For (c) we know that the water in liquid state and at normal atmospheric pressure exists between 0 and 100 Celsius.

Therefore the range will be

Rang (C) = (0,100)

Now, we need to find the domain for this range. We do this by equaliting and finding the value for the variable ''F'' :

For C = 0 :

⇒

And for C = 100 :

⇒

Therefore, the domain as relating temperatures of water in its liquid state is

Dom (C) = (32,212)

For (d) we only need to replace in the equation by and find the value of C ⇒

⇒

≅ 21.67

C(71) = 21.67 °C