Find the inverse function in slope-intercept form (mx+b) : f(x)=2x-8 Answer: f^(-1)(x)=

Understand Inverse Function Concept: Understand the concept of an inverse function. An inverse function essentially reverses the operation of the original function. If f(x) takes an input x and produces an output y, then the inverse function f^(-1)(x) takes y as an input and produces the original x as an output.Write Original Function: Write the original function. The original function is f(x) = 2x - 8. To find the inverse, we need to solve for x in terms of y.Swap x and y: Swap x and y. To find the inverse function, we switch the roles of x and y. This means we will replace f(x) with y and then solve for x. So, we have y = 2x - 8.Solve for x: Solve for x. Now we need to solve the equation y = 2x - 8 for x. Add 8 to both sides of the equation to isolate the term with x on one side: y + 8 = 2x.Divide by 2: Divide by 2. To solve for x, divide both sides of the equation by 2: (y + 8) / 2 = x.Write Inverse Function: Write the inverse function. Now that we have x in terms of y, we can write the inverse function. Replace x with f^(-1)(x) and y with x to get the inverse function in terms of x. f^(-1)(x) = (x + 8) / 2.Convert to Slope-Intercept Form: Convert to slope-intercept form. The slope-intercept form is y = mx + b. Our inverse function is already in this form, with m = 1/2 and b = 8/2. So, f^(-1)(x) = 1/2 * x + 4.

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Find the inverse function in slope-intercept form
(mx+b) :

f(x)=2x-8
Answer:
f^(-1)(x)=

Find the inverse function in slope-intercept form $(\mathrm{mx}+\mathrm{b})$ : $\newline$ $f(x)=2 x-8$ $\newline$ Answer: $f^{-1}(x)=$

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Q. Find the inverse function in slope-intercept form

(\mathrm{mx}+\mathrm{b})

\newline

f(x)=2 x-8

\newline

Answer:

f^{-1}(x)=

Understand Inverse Function Concept: Understand the concept of an inverse function. An inverse function essentially reverses the operation of the original function. If $f(x)$ takes an input $x$ and produces an output $y$ , then the inverse function $f^{-1}(x)$ takes $y$ as an input and produces the original $x$ as an output.
Write Original Function: Write the original function. $\newline$ The original function is $f(x) = 2x - 8$ . To find the inverse, we need to solve for $x$ in terms of $y$ .
Swap x and y: Swap x and y. $\newline$ To find the inverse function, we switch the roles of x and y. This means we will replace $f(x)$ with $y$ and then solve for $x$ . $\newline$ So, we have $y = 2x - 8$ .
Solve for x: Solve for x. $\newline$ Now we need to solve the equation $y = 2x - 8$ for $x$ . $\newline$ Add $8$ to both sides of the equation to isolate the term with $x$ on one side: $y + 8 = 2x$ .
Divide by $2$ : Divide by ext{ extdollar} $2$ ext{ extdollar}. $\newline$ To solve for ext{ extdollar}x ext{ extdollar}, divide both sides of the equation by ext{ extdollar} $2$ ext{ extdollar}: ext{ extdollar}rac{y + $8$ }{ $2$ } = x ext{ extdollar}.
Write Inverse Function: Write the inverse function. $\newline$ Now that we have $x$ in terms of $y$ , we can write the inverse function. Replace $x$ with $f^{-1}(x)$ and $y$ with $x$ to get the inverse function in terms of $x$ . $\newline$ $f^{-1}(x) = \frac{x + 8}{2}$ .
Convert to Slope-Intercept Form: Convert to slope-intercept form. $\newline$ The slope-intercept form is $y = mx + b$ . Our inverse function is already in this form, with $m = \frac{1}{2}$ and $b = \frac{8}{2}$ . $\newline$ So, $f^{-1}(x) = \frac{1}{2} \times x + 4$ .