For the function f(x)=(10+3x)/(1-4x), find f^(-1)(x). Answer: f^(-1)(x)=

Replace with 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's start by replacing f(x) with y: y = (10 + 3x) / (1 - 4x)Interchange x and y: Now, interchange x and y to find the inverse: x = (10 + 3y) / (1 - 4y)Eliminate the fraction: Next, we need to solve for y. Start by multiplying both sides of the equation by (1 - 4y) to eliminate the fraction: x * (1 - 4y) = 10 + 3yMove terms around: Distribute x on the left side of the equation: x - 4xy = 10 + 3yFactor out y: Now, we want to get all the terms with y on one side and the constant terms on the other side. Let's move the 3y term to the left side and the x term to the right side: 4xy + 3y = 10 - xDivide to solve for y: Factor out y from the left side of the equation: y(4x + 3) = 10 - xFinal Inverse Function: Now, divide both sides by (4x + 3) to solve for y: y = (10 - x) / (4x + 3)We have found the inverse function. Therefore, the inverse function f^(-1)(x) is: f^(-1)(x) = (10 - x) / (4x + 3)

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For the function
f(x)=(10+3x)/(1-4x), find
f^(-1)(x).
Answer:
f^(-1)(x)=

For the function $f(x)=\frac{10+3 x}{1-4 x}$ , find $f^{-1}(x)$ . $\newline$ Answer: $f^{-1}(x)=$

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Algebra 2

Write a formula for an arithmetic sequence

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Q. For the function

f(x)=\frac{10+3 x}{1-4 x}

, find

f^{-1}(x)

\newline

Answer:

f^{-1}(x)=

Replace with 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's start by replacing $f(x)$ with $y$ : $y = \frac{10 + 3x}{1 - 4x}$
Interchange x and y: Now, interchange x and y to find the inverse: $x = \frac{10 + 3y}{1 - 4y}$
Eliminate the fraction: Next, we need to solve for $y$ . Start by multiplying both sides of the equation by $(1 - 4y)$ to eliminate the fraction: $\newline$ $x \cdot (1 - 4y) = 10 + 3y$
Move terms around: Distribute $x$ on the left side of the equation: $\newline$ $x - 4xy = 10 + 3y$
Factor out $y$ : Now, we want to get all the terms with $y$ on one side and the constant terms on the other side. Let's move the $3y$ term to the left side and the $x$ term to the right side: $\newline$ $4xy + 3y = 10 - x$
Divide to solve for y: Factor out y from the left side of the equation: $\newline$ $y(4x + 3) = 10 - x$
Final Inverse Function: Now, divide both sides by $(4x + 3)$ to solve for $y$ : $y = \frac{10 - x}{4x + 3}$
Final Inverse Function: Now, divide both sides by $(4x + 3)$ to solve for $y$ : $y = \frac{10 - x}{4x + 3}$ We have found the inverse function. Therefore, the inverse function $f^{-1}(x)$ is: $f^{-1}(x) = \frac{10 - x}{4x + 3}$