QuestionFind the inverse function of $f(x)=6x+14$ . What is $f^{-1}(x)$ ?

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is given by $f(x) =6x +14$ . . We are asked to find the inverse of this function, denoted as $f^{-1}(x)$ .

STEP 2

The inverse of a function $f(x)$ is found by swapping $x$ and $y$ and then solving for $y$ . So, we start by writing the function as $y =6x +14$ .

STEP 3

Swap $x$ and $y$ in the equation.
$x =6y +14$

STEP 4

Now, solve the equation for $y$ to find $f^{-1}(x)$ . Start by subtracting14 from both sides of the equation.
$x -14 =6y$

STEP 5

Next, divide both sides of the equation by to solve for $y$ .
$y = \frac{x -14}{}$

STEP 6

So, the inverse of the function $f(x)$ , denoted as $f^{-1}(x)$ , is given by $f^{-1}(x) = \frac{x -14}{6}$ The inverse of the function $f(x) =6x +14$ is $f^{-1}(x) = \frac{x -14}{6}$ .

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QuestionFind the inverse function of $f(x)=6x+14$ . What is $f^{-1}(x)$ ?

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is given by $f(x) =6x +14$ . . We are asked to find the inverse of this function, denoted as $f^{-1}(x)$ .

STEP 2

The inverse of a function $f(x)$ is found by swapping $x$ and $y$ and then solving for $y$ . So, we start by writing the function as $y =6x +14$ .

STEP 3

Swap $x$ and $y$ in the equation.
$x =6y +14$

STEP 4

Now, solve the equation for $y$ to find $f^{-1}(x)$ . Start by subtracting14 from both sides of the equation.
$x -14 =6y$

STEP 5

Next, divide both sides of the equation by to solve for $y$ .
$y = \frac{x -14}{}$

STEP 6

So, the inverse of the function $f(x)$ , denoted as $f^{-1}(x)$ , is given by $f^{-1}(x) = \frac{x -14}{6}$ The inverse of the function $f(x) =6x +14$ is $f^{-1}(x) = \frac{x -14}{6}$ .

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QuestionFind the inverse function of f(x)=6x+14f(x)=6x+14f(x)=6x+14. What is f−1(x)f^{-1}(x)f−1(x)?

Studdy Solution

STEP 1

Assumptions1. The function f(x)f(x)f(x) is given by f(x)=6x+14f(x) =6x +14f(x)=6x+14. . We are asked to find the inverse of this function, denoted as f−1(x)f^{-1}(x)f−1(x).

STEP 2

The inverse of a function f(x)f(x)f(x) is found by swapping xxx and yyy and then solving for yyy. So, we start by writing the function as y=6x+14y =6x +14y=6x+14.

STEP 3

Swap xxx and yyy in the equation.x=6y+14x =6y +14x=6y+14

STEP 4

Now, solve the equation for yyy to find f−1(x)f^{-1}(x)f−1(x). Start by subtracting14 from both sides of the equation.x−14=6yx -14 =6yx−14=6y

STEP 5

Next, divide both sides of the equation by to solve for yyy.y=x−14y = \frac{x -14}{}y=x−14​

STEP 6

So, the inverse of the function f(x)f(x)f(x), denoted as f−1(x)f^{-1}(x)f−1(x), is given byf−1(x)=x−146f^{-1}(x) = \frac{x -14}{6}f−1(x)=6x−14​The inverse of the function f(x)=6x+14f(x) =6x +14f(x)=6x+14 is f−1(x)=x−146f^{-1}(x) = \frac{x -14}{6}f−1(x)=6x−14​.

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QuestionFind the inverse function of $f(x)=6x+14$ . What is $f^{-1}(x)$ ?

Assumptions1. The function $f(x)$ is given by $f(x) =6x +14$ . . We are asked to find the inverse of this function, denoted as $f^{-1}(x)$ .

The inverse of a function $f(x)$ is found by swapping $x$ and $y$ and then solving for $y$ . So, we start by writing the function as $y =6x +14$ .

Swap $x$ and $y$ in the equation.
$x =6y +14$

Now, solve the equation for $y$ to find $f^{-1}(x)$ . Start by subtracting14 from both sides of the equation.
$x -14 =6y$

Next, divide both sides of the equation by to solve for $y$ .
$y = \frac{x -14}{}$

So, the inverse of the function $f(x)$ , denoted as $f^{-1}(x)$ , is given by $f^{-1}(x) = \frac{x -14}{6}$ The inverse of the function $f(x) =6x +14$ is $f^{-1}(x) = \frac{x -14}{6}$ .