For the function f(x)=(1)/(7+2x), find f^(-1)(x). Answer: f^(-1)(x)=

Switch Roles of x and y: To find the inverse function, f^(-1)(x), we need to switch the roles of x and y in the original function and then solve for y. Let y = f(x) = (1)/(7+2x) Now switch x and y to get x = (1)/(7+2y)Solve for y: Next, we need to solve for y in the equation x = (1)/(7+2y). To do this, we can start by getting rid of the fraction by multiplying both sides of the equation by (7+2y). x * (7+2y) = 1Multiply by (7+2y): Now distribute the x on the left side of the equation. 7x + 2xy = 1Isolate y: We want to isolate y, so let's move the term without y (7x) to the right side of the equation by subtracting 7x from both sides. 2xy = 1 - 7xDivide by 2x: Now, divide both sides of the equation by 2x to solve for y. y = (1 - 7x) / (2x)Inverse Function: This gives us the inverse function of f(x). f^(-1)(x) = (1 - 7x) / (2x)

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For the function
f(x)=(1)/(7+2x), find
f^(-1)(x).
Answer:
f^(-1)(x)=

For the function $f(x)=\frac{1}{7+2 x}$ , find $f^{-1}(x)$ . $\newline$ Answer: $f^{-1}(x)=$

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Algebra 1

Multiplication with rational exponents

Full solution

Q. For the function

f(x)=\frac{1}{7+2 x}

, find

f^{-1}(x)

\newline

Answer:

f^{-1}(x)=

Switch Roles of x and y: To find the inverse function, $f^{-1}(x)$ , we need to switch the roles of $x$ and $y$ in the original function and then solve for $y$ .
Let $y = f(x) = \frac{1}{7+2x}$
Now switch $x$ and $y$ to get $x = \frac{1}{7+2y}$
Solve for $y$ : Next, we need to solve for $y$ in the equation $x = \frac{1}{7+2y}$ . To do this, we can start by getting rid of the fraction by multiplying both sides of the equation by $(7+2y)$ . $x \cdot (7+2y) = 1$
Multiply by $(7+2y)$ : Now distribute the $x$ on the left side of the equation. $7x + 2xy = 1$
Isolate $y$ : We want to isolate $y$ , so let's move the term without $y$ ( $7x$ ) to the right side of the equation by subtracting $7x$ from both sides. $\newline$ $2xy = 1 - 7x$
Divide by $2x$ : Now, divide both sides of the equation by $2x$ to solve for $y$ . $y = \frac{1 - 7x}{2x}$
Inverse Function: This gives us the inverse function of $f(x)$ . $f^{-1}(x) = \frac{1 - 7x}{2x}$