Find the inverse function of the function f(x)=(1)/(2)x+2. f^(-1)(x)=2x-2 f^(-1)(x)=(1)/(2)x-2 f^(-1)(x)=2x-4 f^(-1)(x)=(1)/(2)x-4

Understand the problem: Understand the problem. We need to find the inverse function of f(x) = (1/2)x + 2. The inverse function, denoted as f^(-1)(x), will undo the operation done by f(x). To find the inverse, we will switch the roles of x and y and solve for y.Replace with y: Replace f(x) with y. Let y = (1/2)x + 2. This is the first step in finding the inverse function.Swap x and y: Swap x and y. Now we will replace y with x and x with y to find the inverse function. So we get x = (1/2)y + 2.Solve for y: Solve for y. To solve for y, we need to isolate y on one side of the equation. First, we subtract 2 from both sides to get x - 2 = (1/2)y.Multiply by 2: Multiply both sides by 2. To get y by itself, we multiply both sides of the equation by 2. This gives us 2(x - 2) = y.Distribute and simplify: Distribute and simplify. We distribute the 2 on the left side of the equation to get 2x - 4 = y.Write inverse function: Write the inverse function. Now that we have y by itself, we can write the inverse function as f^(-1)(x) = 2x - 4.

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Find the inverse function of the function
f(x)=(1)/(2)x+2.

f^(-1)(x)=2x-2

f^(-1)(x)=(1)/(2)x-2

f^(-1)(x)=2x-4

f^(-1)(x)=(1)/(2)x-4

Find the inverse function of the function $f(x)=\frac{1}{2} x+2$ . $\newline$ $f^{-1}(x)=2 x-2$ $\newline$ $f^{-1}(x)=\frac{1}{2} x-2$ $\newline$ $f^{-1}(x)=2 x-4$ $\newline$ $f^{-1}(x)=\frac{1}{2} x-4$

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Math Problems

Algebra 1

Multiplication with rational exponents

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Q. Find the inverse function of the function

f(x)=\frac{1}{2} x+2

\newline

f^{-1}(x)=2 x-2

\newline

f^{-1}(x)=\frac{1}{2} x-2

\newline

f^{-1}(x)=2 x-4

\newline

f^{-1}(x)=\frac{1}{2} x-4

Understand the problem: Understand the problem. $\newline$ We need to find the inverse function of $f(x) = \frac{1}{2}x + 2$ . The inverse function, denoted as $f^{-1}(x)$ , will undo the operation done by $f(x)$ . To find the inverse, we will switch the roles of $x$ and $y$ and solve for $y$ .
Replace with $y$ : Replace $f(x)$ with $y$ . $\newline$ Let $y = \frac{1}{2}x + 2$ . This is the first step in finding the inverse function.
Swap $x$ and $y$ : Swap $x$ and $y$ . Now we will replace $y$ with $x$ and $x$ with $y$ to find the inverse function. So we get $x = (\frac{1}{2})y + 2$ .
Solve for y: Solve for y. $\newline$ To solve for y, we need to isolate y on one side of the equation. First, we subtract $2$ from both sides to get $x - 2 = (\frac{1}{2})y$ .
Multiply by $2$ : Multiply both sides by $2$ . $\newline$ To get $y$ by itself, we multiply both sides of the equation by $2$ . This gives us $2(x - 2) = y$ .
Distribute and simplify: Distribute and simplify. $\newline$ We distribute the $2$ on the left side of the equation to get $2x - 4 = y$ .
Write inverse function: Write the inverse function. $\newline$ Now that we have $y$ by itself, we can write the inverse function as $f^{-1}(x) = 2x - 4$ .