QuestionFind the inverse of the function $f(x)=\frac{9}{5}x+32$ that converts Celsius to Fahrenheit.

Studdy Solution

STEP 1

Assumptions1. The function f(x) = \frac{9}{5}x +32 converts temperatures from Celsius to Fahrenheit. . We are asked to find the inverse of this function, which will convert temperatures from Fahrenheit to Celsius.

STEP 2

First, let's write down the function we are given.
$f(x) = \frac{9}{5}x +32$

STEP 3

To find the inverse of a function, we first replace the function notation f(x) with y. This gives us $y = \frac{9}{5}x +32$

STEP 4

The next step in finding the inverse of a function is to swap x and y. This gives us $x = \frac{9}{}y +32$

STEP 5

Now, we need to solve this equation for y to get the inverse function. First, we subtract32 from both sides $x -32 = \frac{9}{5}y$

STEP 6

Next, we multiply both sides by \frac{5}{9} to isolate y $y = \frac{5}{9}(x -32)$

STEP 7

This is the inverse function, which we can write as $f^{-1}(x) = \frac{5}{9}(x -32)$ So, the inverse of the function f(x) = \frac{9}{5}x +32 is f^{-1}(x) = \frac{5}{9}(x -32). This function converts temperatures from Fahrenheit to Celsius.

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QuestionFind the inverse of the function $f(x)=\frac{9}{5}x+32$ that converts Celsius to Fahrenheit.

Studdy Solution

STEP 1

Assumptions1. The function f(x) = \frac{9}{5}x +32 converts temperatures from Celsius to Fahrenheit. . We are asked to find the inverse of this function, which will convert temperatures from Fahrenheit to Celsius.

STEP 2

First, let's write down the function we are given.
$f(x) = \frac{9}{5}x +32$

STEP 3

To find the inverse of a function, we first replace the function notation f(x) with y. This gives us $y = \frac{9}{5}x +32$

STEP 4

The next step in finding the inverse of a function is to swap x and y. This gives us $x = \frac{9}{}y +32$

STEP 5

Now, we need to solve this equation for y to get the inverse function. First, we subtract32 from both sides $x -32 = \frac{9}{5}y$

STEP 6

Next, we multiply both sides by \frac{5}{9} to isolate y $y = \frac{5}{9}(x -32)$

STEP 7

This is the inverse function, which we can write as $f^{-1}(x) = \frac{5}{9}(x -32)$ So, the inverse of the function f(x) = \frac{9}{5}x +32 is f^{-1}(x) = \frac{5}{9}(x -32). This function converts temperatures from Fahrenheit to Celsius.

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QuestionFind the inverse of the function f(x)=95x+32f(x)=\frac{9}{5}x+32f(x)=59​x+32 that converts Celsius to Fahrenheit.

Studdy Solution

STEP 1

Assumptions1. The function f(x) = \frac{9}{5}x +32 converts temperatures from Celsius to Fahrenheit. . We are asked to find the inverse of this function, which will convert temperatures from Fahrenheit to Celsius.

STEP 2

First, let's write down the function we are given.f(x)=95x+32f(x) = \frac{9}{5}x +32f(x)=59​x+32

STEP 3

To find the inverse of a function, we first replace the function notation f(x) with y. This gives usy=95x+32y = \frac{9}{5}x +32y=59​x+32

STEP 4

The next step in finding the inverse of a function is to swap x and y. This gives usx=9y+32x = \frac{9}{}y +32x=9​y+32

STEP 5

Now, we need to solve this equation for y to get the inverse function. First, we subtract32 from both sidesx−32=95yx -32 = \frac{9}{5}yx−32=59​y

STEP 6

Next, we multiply both sides by \frac{5}{9} to isolate yy=59(x−32)y = \frac{5}{9}(x -32)y=95​(x−32)

STEP 7

This is the inverse function, which we can write asf−1(x)=59(x−32)f^{-1}(x) = \frac{5}{9}(x -32)f−1(x)=95​(x−32)So, the inverse of the function f(x) = \frac{9}{5}x +32 is f^{-1}(x) = \frac{5}{9}(x -32). This function converts temperatures from Fahrenheit to Celsius.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the inverse of the function $f(x)=\frac{9}{5}x+32$ that converts Celsius to Fahrenheit.

First, let's write down the function we are given.
$f(x) = \frac{9}{5}x +32$

To find the inverse of a function, we first replace the function notation f(x) with y. This gives us $y = \frac{9}{5}x +32$

The next step in finding the inverse of a function is to swap x and y. This gives us $x = \frac{9}{}y +32$

Now, we need to solve this equation for y to get the inverse function. First, we subtract32 from both sides $x -32 = \frac{9}{5}y$

Next, we multiply both sides by \frac{5}{9} to isolate y $y = \frac{5}{9}(x -32)$

This is the inverse function, which we can write as $f^{-1}(x) = \frac{5}{9}(x -32)$ So, the inverse of the function f(x) = \frac{9}{5}x +32 is f^{-1}(x) = \frac{5}{9}(x -32). This function converts temperatures from Fahrenheit to Celsius.