Given the equation:
[tex]T\mleft(h\mright)=48.5-2.5h[/tex]
where: (h) is the height above the planet's surface in kilometers.
T(h) is the temperature in Celsius.
If we have calculated the function:
[tex]h=T^{-1}(x)[/tex]
(a)
so, the output is the last function will be the height above the planet's surface.
So, the statements that best describe the last function is:
(b) the expression for the last function will be as follows:
[tex]\begin{gathered} x=48.5-2.5h \\ 2.5h=48.5-x \\ h=\frac{1}{2.5}(48.5-x) \\ \\ h=19.4-0.4x \end{gathered}[/tex]
so, the answer for part (b) is:
[tex]T^{-1}(x)=19.4-0.4x[/tex]
Part (c): we need to find:
[tex]T^{-1}(33)=\text{?}[/tex]
So, By substitution with x = 33 into the equation of part (a) as follows:
[tex]\begin{gathered} T^{-1}(33)=19.4-0.4\cdot33 \\ \\ T^{-1}(33)=6.2 \end{gathered}[/tex]
so, the answer of part (c) = 6.2