To find the inverse of the function [tex]\( F(C) = \frac{9}{5} C + 32 \)[/tex], we need to express [tex]\( C \)[/tex] in terms of [tex]\( F \)[/tex]. Let's go through the steps:
1. Start with the given function:
[tex]\[
F = \frac{9}{5} C + 32
\][/tex]
2. Subtract 32 from both sides to isolate the term involving [tex]\( C \)[/tex]:
[tex]\[
F - 32 = \frac{9}{5} C
\][/tex]
3. Multiply both sides of the equation by [tex]\(\frac{5}{9}\)[/tex] to solve for [tex]\( C \)[/tex]:
[tex]\[
C = \frac{5}{9}(F - 32)
\][/tex]
Therefore, the inverse function is:
[tex]\[
C(F) = \frac{5}{9}F - \frac{5}{9} \cdot 32
\][/tex]
We can simplify the constant term:
[tex]\[
C(F) = \frac{5}{9}F - \frac{160}{9}
\][/tex]
Thus, the inverse of [tex]\( F(C) = \frac{9}{5} C + 32 \)[/tex] is:
[tex]\[
C(F) = \frac{5}{9} F - \frac{160}{9}
\][/tex]
So the inverse function [tex]\( C(F) \)[/tex] is:
[tex]\[
\boxed{C(F) = 0.5555555555555556F - \frac{160}{9}}
\][/tex]
When written directly in the given form:
[tex]\[
C(F) = \boxed{0.5555555555555556} F - \boxed{\frac{160}{9}}
\][/tex]
