Question

Finding, evaluating, and interpreting an inverse function for a given linear relationship

Answer 1

Given relationship is

`T(h)=38-1.25h`

Suppose,

`x=T(h)`

(b). Now,

`\begin{gathered} x=38-1.25h \\ 1.25h=38-x \\ h=(38-x)/(1.25) \end{gathered}`

Thus,

`T^(-1)(x)=(38-x)/(1.25)`

(a). The function

`T^(-1)(x)`

Represents the height above the surface when the temperature is x degree celsius.

(c). Putting x=25

`\begin{gathered} T^(-1)(25)=(38-25)/(1.25) \\ T^(-1)(25)=10.4 \end{gathered}`

Hence, the desired value is 10.4.