QuestionFind the inverse of the one-to-one function $f(x) = 8x$ .

Studdy Solution

STEP 1

Assumptions1. The function $f$ is one-to-one, which means that for every $y$ there is exactly one $x$ such that $f(x) = y$ . . The function $f$ is given by $f(x) =8x$ .

STEP 2

To find the inverse of a function, we first replace the function notation $f(x)$ with $y$ .
$y =8x$

STEP 3

Next, we switch the roles of $x$ and $y$ . This means we interchange $x$ and $y$ in the equation.
$x =8y$

STEP 4

Now, we solve the equation for $y$ to get the inverse function. In this case, we divide both sides of the equation by8.
$y = \frac{x}{8}$

STEP 5

Finally, we replace $y$ with $f^{-1}(x)$ , which denotes the inverse function of $f$ .
$f^{-1}(x) = \frac{x}{8}$ So, the inverse of the function $f(x) =8x$ is $f^{-1}(x) = \frac{x}{8}$ .

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QuestionFind the inverse of the one-to-one function $f(x) = 8x$ .

Studdy Solution

STEP 1

Assumptions1. The function $f$ is one-to-one, which means that for every $y$ there is exactly one $x$ such that $f(x) = y$ . . The function $f$ is given by $f(x) =8x$ .

STEP 2

To find the inverse of a function, we first replace the function notation $f(x)$ with $y$ .
$y =8x$

STEP 3

Next, we switch the roles of $x$ and $y$ . This means we interchange $x$ and $y$ in the equation.
$x =8y$

STEP 4

Now, we solve the equation for $y$ to get the inverse function. In this case, we divide both sides of the equation by8.
$y = \frac{x}{8}$

STEP 5

Finally, we replace $y$ with $f^{-1}(x)$ , which denotes the inverse function of $f$ .
$f^{-1}(x) = \frac{x}{8}$ So, the inverse of the function $f(x) =8x$ is $f^{-1}(x) = \frac{x}{8}$ .

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QuestionFind the inverse of the one-to-one function f(x)=8xf(x) = 8xf(x)=8x.

Studdy Solution

STEP 1

Assumptions1. The function fff is one-to-one, which means that for every yyy there is exactly one xxx such that f(x)=yf(x) = yf(x)=y. . The function fff is given by f(x)=8xf(x) =8xf(x)=8x.

STEP 2

To find the inverse of a function, we first replace the function notation f(x)f(x)f(x) with yyy.y=8xy =8xy=8x

STEP 3

Next, we switch the roles of xxx and yyy. This means we interchange xxx and yyy in the equation.x=8yx =8yx=8y

STEP 4

Now, we solve the equation for yyy to get the inverse function. In this case, we divide both sides of the equation by8.y=x8y = \frac{x}{8}y=8x​

STEP 5

Finally, we replace yyy with f−1(x)f^{-1}(x)f−1(x), which denotes the inverse function of fff.f−1(x)=x8f^{-1}(x) = \frac{x}{8}f−1(x)=8x​So, the inverse of the function f(x)=8xf(x) =8xf(x)=8x is f−1(x)=x8f^{-1}(x) = \frac{x}{8}f−1(x)=8x​.

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QuestionFind the inverse of the one-to-one function $f(x) = 8x$ .

Assumptions1. The function $f$ is one-to-one, which means that for every $y$ there is exactly one $x$ such that $f(x) = y$ . . The function $f$ is given by $f(x) =8x$ .

To find the inverse of a function, we first replace the function notation $f(x)$ with $y$ .
$y =8x$

Next, we switch the roles of $x$ and $y$ . This means we interchange $x$ and $y$ in the equation.
$x =8y$

Now, we solve the equation for $y$ to get the inverse function. In this case, we divide both sides of the equation by8.
$y = \frac{x}{8}$

Finally, we replace $y$ with $f^{-1}(x)$ , which denotes the inverse function of $f$ .
$f^{-1}(x) = \frac{x}{8}$ So, the inverse of the function $f(x) =8x$ is $f^{-1}(x) = \frac{x}{8}$ .