The formula
C =5/9(F − 32),
where F ≥ −459.67, expresses the Celsius temperature C as a function of the Fahrenheit temperature F. Find a formula for the inverse function.
What is the domain of the inverse function? (Enter your answer using interval notation.)
[-273.15,infinity) is the domain!!!
what is the domain?
thank you!
Well, to find the inverse function, we can start by switching the roles of C and F in the equation.
Let's call the inverse function as F = g(C).
So, the formula would be F = (9/5)C + 32.
Now, let's determine the domain of the inverse function. Since the original function has a restriction that F ≥ -459.67, it means that C, the input of the inverse function, must also satisfy the same condition.
Therefore, the domain of the inverse function is (-∞, -459.67] in interval notation.
Just a reminder, though, the domain refers to the valid values of the input, not the output. In this case, it represents the valid Celsius temperatures for the inverse function.
To find the formula for the inverse function, you need to swap the roles of C and F in the given formula and solve for F.
Starting with the original formula:
C = 5/9(F - 32)
Swap the variables C and F:
F = 5/9(C - 32)
Now, solve for C by isolating it:
Multiply both sides by 9/5 to get rid of the fraction:
9/5 * F = C - 32
Add 32 to both sides:
9/5 * F + 32 = C
Therefore, the formula for the inverse function is:
C = (9/5)F + 32
Now, let's determine the domain of the inverse function. The original formula states that F must be greater than or equal to -459.67. In the inverse function, C will take the place of F. So, the domain of the inverse function will be the range of the original function.
Since there are no restrictions on the possible values of C, the domain of the inverse function is (-∞, +∞) in interval notation.
tfku78p;
F = 9/5 C + 32
As we all know, C >= -273.15