Find a formula for the inverse of the function
described below.
16) Fahrenheit = Celsius. A function
that converts temperatures in Fahreaheit
to those in Celsius is .

Ask by Mcdonald Nguyen. in the United States

Mar 20,2025

Question

Find a formula for the inverse of the function
described below.
16) Fahrenheit = Celsius. A function
that converts temperatures in Fahreaheit
to those in Celsius is .

Ask by Mcdonald Nguyen. in the United States

Mar 20,2025

UpStudy AI · Accepted Answer

To find the inverse of the function $$ f(x) = \frac{5}{9}(x - 32) $$, we will follow these steps:

1. **Replace $$ f(x) $$ with $$ y $$**:
   $$
   y = \frac{5}{9}(x - 32)
   $$

2. **Swap $$ x $$ and $$ y $$**:
   $$
   x = \frac{5}{9}(y - 32)
   $$

3. **Solve for $$ y $$**:
   - First, multiply both sides by $$ 9 $$:
   $$
   9x = 5(y - 32)
   $$
   - Next, divide both sides by $$ 5 $$:
   $$
   \frac{9x}{5} = y - 32
   $$
   - Finally, add $$ 32 $$ to both sides:
   $$
   y = \frac{9x}{5} + 32
   $$

4. **Replace $$ y $$ with $$ f^{-1}(x) $$**:
   $$
   f^{-1}(x) = \frac{9x}{5} + 32
   $$

Thus, the formula for the inverse of the function is:
$$
f^{-1}(x) = \frac{9x}{5} + 32
$$
The inverse function is $$ f^{-1}(x) = \frac{9x}{5} + 32 $$.

Find a formula for the inverse of the function
described below.
16) Fahrenheit = Celsius. A function
that converts temperatures in Fahreaheit
to those in Celsius is .

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Solución

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Find a formula for the inverse of the function described below. 16) Fahrenheit = Celsius. A function that converts temperatures in Fahreaheit to those in Celsius is .

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Find a formula for the inverse of the function
described below.
16) Fahrenheit = Celsius. A function
that converts temperatures in Fahreaheit
to those in Celsius is .