QuestionFind the inverse function of $f(x)=13-x$ . What is $f^{-1}(x)$ ?

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=13-x$ . We are asked to find the inverse of this function, denoted as $f^{-1}(x)$

STEP 2

To find the inverse of a function, we first replace $f(x)$ with $y$ . This gives us $y =13 - x$

STEP 3

Next, we swap $x$ and $y$ . This means we replace every $x$ with $y$ and vice versa $x =13 - y$

STEP 4

Now, we solve for $y$ to get the inverse function. To do this, we subtract $13$ from both sides and multiply by $-1$ $y =13 - x$ $-y = x -13$ $y = -x +13$

STEP 5

Finally, we replace $y$ with $f^{-1}(x)$ to denote that this is the inverse function $f^{-1}(x) = -x +13$ So, the inverse of the function $f(x)=13-x$ is $f^{-1}(x)=-x+13$ .

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QuestionFind the inverse function of $f(x)=13-x$ . What is $f^{-1}(x)$ ?

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=13-x$ . We are asked to find the inverse of this function, denoted as $f^{-1}(x)$

STEP 2

To find the inverse of a function, we first replace $f(x)$ with $y$ . This gives us $y =13 - x$

STEP 3

Next, we swap $x$ and $y$ . This means we replace every $x$ with $y$ and vice versa $x =13 - y$

STEP 4

Now, we solve for $y$ to get the inverse function. To do this, we subtract $13$ from both sides and multiply by $-1$ $y =13 - x$ $-y = x -13$ $y = -x +13$

STEP 5

Finally, we replace $y$ with $f^{-1}(x)$ to denote that this is the inverse function $f^{-1}(x) = -x +13$ So, the inverse of the function $f(x)=13-x$ is $f^{-1}(x)=-x+13$ .

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QuestionFind the inverse function of f(x)=13−xf(x)=13-xf(x)=13−x. What is f−1(x)f^{-1}(x)f−1(x)?

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=13−xf(x)=13-xf(x)=13−x . We are asked to find the inverse of this function, denoted as f−1(x)f^{-1}(x)f−1(x)

STEP 2

To find the inverse of a function, we first replace f(x)f(x)f(x) with yyy. This gives usy=13−xy =13 - xy=13−x

STEP 3

Next, we swap xxx and yyy. This means we replace every xxx with yyy and vice versax=13−yx =13 - yx=13−y

STEP 4

Now, we solve for yyy to get the inverse function. To do this, we subtract 131313 from both sides and multiply by −1-1−1y=13−xy =13 - xy=13−x−y=x−13-y = x -13−y=x−13y=−x+13y = -x +13y=−x+13

STEP 5

Finally, we replace yyy with f−1(x)f^{-1}(x)f−1(x) to denote that this is the inverse functionf−1(x)=−x+13f^{-1}(x) = -x +13f−1(x)=−x+13So, the inverse of the function f(x)=13−xf(x)=13-xf(x)=13−x is f−1(x)=−x+13f^{-1}(x)=-x+13f−1(x)=−x+13.

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QuestionFind the inverse function of $f(x)=13-x$ . What is $f^{-1}(x)$ ?

Assumptions1. The function is $f(x)=13-x$ . We are asked to find the inverse of this function, denoted as $f^{-1}(x)$

To find the inverse of a function, we first replace $f(x)$ with $y$ . This gives us $y =13 - x$

Next, we swap $x$ and $y$ . This means we replace every $x$ with $y$ and vice versa $x =13 - y$

Now, we solve for $y$ to get the inverse function. To do this, we subtract $13$ from both sides and multiply by $-1$ $y =13 - x$ $-y = x -13$ $y = -x +13$

Finally, we replace $y$ with $f^{-1}(x)$ to denote that this is the inverse function $f^{-1}(x) = -x +13$ So, the inverse of the function $f(x)=13-x$ is $f^{-1}(x)=-x+13$ .