For the function f(x)=(7-4x)/(10+3x), find f^(-1)(x). Answer: f^(-1)(x)=

Question

For the function  f(x)=(7-4x)/(10+3x), find  f^(-1)(x). Answer:  f^(-1)(x)=

Bytelearn · Accepted Answer

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 to make it easier to work with. y = (7 - 4x) / (10 + 3x)Switch x and y: Now, switch x and y to find the inverse function. x = (7 - 4y) / (10 + 3y)Multiply both sides: Next, we need to solve for y. To do this, we'll multiply both sides of the equation by (10 + 3y) to get rid of the fraction. x * (10 + 3y) = 7 - 4yDistribute x: Distribute x on the left side of the equation. 10x + 3xy = 7 - 4yMove terms with 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 terms involving y to the left side and the constant to the right side. 3xy + 4y = 7 - 10xFactor out y: Factor out y from the left side of the equation. y(3x + 4) = 7 - 10xDivide both sides: Now, divide both sides by (3x + 4) to solve for y. y = (7 - 10x) / (3x + 4)Find inverse function: We have found the inverse function. Therefore, the inverse function f^(-1)(x) is: f^(-1)(x) = (7 - 10x) / (3x + 4)

For the function $f(x)=\frac{7-4 x}{10+3 x}$ , find $f^{-1}(x)$ . $\newline$ Answer: $f^{-1}(x)=$

Full solution

More problems from Simplify variable expressions using properties

Related topics

For the function f(x)=7−4x10+3x f(x)=\frac{7-4 x}{10+3 x} f(x)=10+3x7−4x​, find f−1(x) f^{-1}(x) f−1(x).\newlineAnswer: f−1(x)= f^{-1}(x)= f−1(x)=

For the function $f(x)=\frac{7-4 x}{10+3 x}$ , find $f^{-1}(x)$ . $\newline$ Answer: $f^{-1}(x)=$