Question

The relationship between the Fahrenheit (F) and Celsius (C) scales is given by

F = g(C) = 9/5C + 32
(a) Find g−1.
g−1(F) =
(b) Find g−1(41).
g−1(41)=

Answer 1

The relationship between Fahrenheit and Celsius scales is given by the equation F = (9/5)C + 32. The inverse function g-1(F) is (F - 32) / (9/5). g-1(41) = 5.

Step-by-step explanation:

The relationship between the Fahrenheit (F) and Celsius (C) scales is given by the equation F = Κ(C) = (9/5)C + 32. To find the inverse function g-1, we need to solve the equation for C in terms of F.

(a) To find g-1(F), we can rearrange the equation F = (9/5)C + 32 to solve for C: (F - 32) / (9/5) = C. Therefore, the inverse function g-1(F) is (F - 32) / (9/5).

(b) To find g-1(41), we substitute F = 41 into the inverse function: g-1(41) = (41 - 32) / (9/5) = 9 / (9/5) = 9 * (5/9) = 5.

Answer 2

To find g-1(F), rearrange the equation to isolate C, and substitute F = 41 into the equation.

Step-by-step explanation:

To find g-1(F), we need to solve the equation for C.

Start with the equation for F = g(C), which is F = 9/5C + 32.

Rearrange the equation to solve for C:

9/5C = F - 32

Multiply both sides by 5/9 to isolate C:

C = (5/9)(F - 32)

Therefore, g-1(F) = (5/9)(F - 32).

To find g-1(41), substitute F = 41 into the equation:

g-1(41) = (5/9)(41 - 32) = (5/9)(9) = 5.