For the function f(x)=(2)/(4+3x), find f^(-1)(x). Answer: f^(-1)(x)=

Rewrite function 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 rewriting the function with y instead of f(x): y = (2)/(4+3x)Switch x and y: Now, switch x and y to find the inverse: x = (2)/(4+3y)Cross-multiply to eliminate fraction: Next, we need to solve for y. To do this, we'll start by cross-multiplying to get rid of the fraction: x * (4 + 3y) = 2Distribute x on left side: Distribute x on the left side of the equation: 4x + 3xy = 2Move term without y: We want to isolate the term with y, so let's move the term without y (4x) to the other side of the equation: 3xy = 2 - 4xDivide both sides to solve for y: Now, divide both sides by 3x to solve for y: y = (2 - 4x) / (3x)Expression for inverse function: This is the expression for the inverse function. Therefore, the inverse function f^(-1)(x) is: f^(-1)(x) = (2 - 4x) / (3x)

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For the function
f(x)=(2)/(4+3x), find
f^(-1)(x).
Answer:
f^(-1)(x)=

For the function $f(x)=\frac{2}{4+3 x}$ , find $f^{-1}(x)$ . $\newline$ Answer: $f^{-1}(x)=$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. For the function

f(x)=\frac{2}{4+3 x}

, find

f^{-1}(x)

\newline

Answer:

f^{-1}(x)=

Rewrite function 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 rewriting the function with $y$ instead of $f(x)$ : $\newline$ $y = \frac{2}{4+3x}$
Switch x and y: Now, switch x and y to find the inverse: $x = \frac{2}{4+3y}$
Cross-multiply to eliminate fraction: Next, we need to solve for $y$ . To do this, we'll start by cross-multiplying to get rid of the fraction: $\newline$ $x \times (4 + 3y) = 2$
Distribute $x$ on left side: Distribute $x$ on the left side of the equation: $4x + 3xy = 2$
Move term without y: We want to isolate the term with $y$ , so let's move the term without $y$ ( $4x$ ) to the other side of the equation: $\newline$ $3xy = 2 - 4x$
Divide both sides to solve for y: Now, divide both sides by $3x$ to solve for $y$ : $\newline$ $y = \frac{2 - 4x}{3x}$
Expression for inverse function: This is the expression for the inverse function. Therefore, the inverse function $f^{-1}(x)$ is: $f^{-1}(x) = \frac{2 - 4x}{3x}$