QuestionFind the inverse function $f^{-1}(x)$ for $f(x) = 8x + 5$ . What is $f^{-1}(x)$ ?

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is given by $f(x) =8x +5$ . We are looking for the inverse function, denoted by $f^{-1}(x)$

STEP 2

The definition of the inverse function is that if $y = f(x)$ , then $x = f^{-1}(y)$ . So, we start by writing $f(x)$ in terms of $y$ .
$y =8x +5$

STEP 3

To find the inverse, we need to solve this equation for $x$ . This means we need to isolate $x$ on one side of the equation.
First, subtract5 from both sides of the equation.
$y -5 =8x$

STEP 4

Next, divide both sides of the equation by8 to solve for $x$ .
$x = \frac{y -}{8}$

STEP 5

Finally, replace $y$ with $x$ to get the inverse function $f^{-1}(x)$ .
$f^{-1}(x) = \frac{x -5}{8}$ So, the inverse of $f$ is $f^{-1}(x) = \frac{x -5}{8}$ .

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QuestionFind the inverse function $f^{-1}(x)$ for $f(x) = 8x + 5$ . What is $f^{-1}(x)$ ?

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is given by $f(x) =8x +5$ . We are looking for the inverse function, denoted by $f^{-1}(x)$

STEP 2

The definition of the inverse function is that if $y = f(x)$ , then $x = f^{-1}(y)$ . So, we start by writing $f(x)$ in terms of $y$ .
$y =8x +5$

STEP 3

To find the inverse, we need to solve this equation for $x$ . This means we need to isolate $x$ on one side of the equation.
First, subtract5 from both sides of the equation.
$y -5 =8x$

STEP 4

Next, divide both sides of the equation by8 to solve for $x$ .
$x = \frac{y -}{8}$

STEP 5

Finally, replace $y$ with $x$ to get the inverse function $f^{-1}(x)$ .
$f^{-1}(x) = \frac{x -5}{8}$ So, the inverse of $f$ is $f^{-1}(x) = \frac{x -5}{8}$ .

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QuestionFind the inverse function f−1(x)f^{-1}(x)f−1(x) for f(x)=8x+5f(x) = 8x + 5f(x)=8x+5. 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)=8x+5f(x) =8x +5f(x)=8x+5 . We are looking for the inverse function, denoted by f−1(x)f^{-1}(x)f−1(x)

STEP 2

The definition of the inverse function is that if y=f(x)y = f(x)y=f(x), then x=f−1(y)x = f^{-1}(y)x=f−1(y). So, we start by writing f(x)f(x)f(x) in terms of yyy.y=8x+5y =8x +5y=8x+5

STEP 3

To find the inverse, we need to solve this equation for xxx. This means we need to isolate xxx on one side of the equation.First, subtract5 from both sides of the equation.y−5=8xy -5 =8xy−5=8x

STEP 4

Next, divide both sides of the equation by8 to solve for xxx.x=y−8x = \frac{y -}{8}x=8y−​

STEP 5

Finally, replace yyy with xxx to get the inverse function f−1(x)f^{-1}(x)f−1(x).f−1(x)=x−58f^{-1}(x) = \frac{x -5}{8}f−1(x)=8x−5​So, the inverse of fff is f−1(x)=x−58f^{-1}(x) = \frac{x -5}{8}f−1(x)=8x−5​.

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QuestionFind the inverse function $f^{-1}(x)$ for $f(x) = 8x + 5$ . What is $f^{-1}(x)$ ?

Assumptions1. The function $f(x)$ is given by $f(x) =8x +5$ . We are looking for the inverse function, denoted by $f^{-1}(x)$

The definition of the inverse function is that if $y = f(x)$ , then $x = f^{-1}(y)$ . So, we start by writing $f(x)$ in terms of $y$ .
$y =8x +5$

To find the inverse, we need to solve this equation for $x$ . This means we need to isolate $x$ on one side of the equation.
First, subtract5 from both sides of the equation.
$y -5 =8x$

Next, divide both sides of the equation by8 to solve for $x$ .
$x = \frac{y -}{8}$

Finally, replace $y$ with $x$ to get the inverse function $f^{-1}(x)$ .
$f^{-1}(x) = \frac{x -5}{8}$ So, the inverse of $f$ is $f^{-1}(x) = \frac{x -5}{8}$ .