Question

MATH HELP!!! 100PTS plus BRAINLIEST!!!!

The formula C=59(F−32), where F≥−459.67 expresses the Celsius temperature C as a function of Fahrenheit temperature F.
1. Find the formula for the inverse function.
Answer: C^−1(F)=
9F/5+32 (I'm right about this one)
2. What is the domain of the inverse function C^−1 ?
Answer (in interval notation):(for some reason it keep telling me wrong :( )

Answer 1

Answer:

$\textsf{1.} \quad C^{-1}(F)=\dfrac{9}{5}F+32$

2.   [-273.15, ∞)

Step-by-step explanation:

Given:

$C=\dfrac{5}{9}(F-32), \quad \text{where }F \geq -459.67$

To find the inverse of the given function, make F the subject:

$\begin{aligned}C & =\dfrac{5}{9}(F-32)\\\implies \dfrac{9}{5}C & =F-32\\\implies F & = \dfrac{9}{5}C+32 \end{aligned}$

$\textsf{Replace the } F \textsf{ with }C^{-1}(F)\textsf{ and the }C \textsf{ with } F:$ :

$\implies C^{-1}(F)=\dfrac{9}{5}F+32$

Domain: set of all possible input values (x-values)

Range: set of all possible output values (y-values)

The given domain of the function C(F) is F ≥ -459.67

Therefore, the minimum value of the function is:

$\implies C(-459.67)=\dffrac{5}{9}(-459.67-32)=-273.15$

This means the range of the function C(F) is C(F) ≥ -273.15

The domain of the inverse function is the range of the function.

Therefore, the domain of the inverse function in interval notation is:  [-273.15, ∞)