For the function f(x)=(5)/(3x+4), find f^(-1)(x). Answer: f^(-1)(x)=

Replace with y: To find the inverse function, we first replace f(x) with y: y = (5)/(3x+4)Swap x and y: Next, we swap x and y to find the inverse: x = (5)/(3y+4)Solve for y: Now, we solve for y to get the inverse function. Multiply both sides by (3y+4) to eliminate the fraction: x(3y+4) = 5Distribute x: Distribute x on the left side: 3xy + 4x = 5Isolate terms with y: Subtract 4x from both sides to isolate terms with y on one side: 3xy = 5 - 4xSolve for y: Divide both sides by 3x to solve for y: y = (5 - 4x) / (3x)Replace y with f^(-1)(x): This is the inverse function, so we replace y with f^(-1)(x): f^(-1)(x) = (5 - 4x) / (3x)

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For the function
f(x)=(5)/(3x+4), find
f^(-1)(x).
Answer:
f^(-1)(x)=

For the function $f(x)=\frac{5}{3 x+4}$ , 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{5}{3 x+4}

, find

f^{-1}(x)

\newline

Answer:

f^{-1}(x)=

Replace with $y$ : To find the inverse function, we first replace $f(x)$ with $y$ : $y = \frac{5}{3x+4}$
Swap x and y: Next, we swap x and y to find the inverse: $x = \frac{5}{3y+4}$
Solve for $y$ : Now, we solve for $y$ to get the inverse function. Multiply both sides by $(3y+4)$ to eliminate the fraction: $\newline$ $x(3y+4) = 5$
Distribute $x$ : Distribute $x$ on the left side: $\newline$ $3xy + 4x = 5$
Isolate terms with $y$ : Subtract $4x$ from both sides to isolate terms with $y$ on one side: $\newline$ $3xy = 5 - 4x$
Solve for y: Divide both sides by $3x$ to solve for y: $\newline$ $y = \frac{5 - 4x}{3x}$
Replace $y$ with $f^{-1}(x)$ : This is the inverse function, so we replace $y$ with $f^{-1}(x)$ : $f^{-1}(x) = \frac{5 - 4x}{3x}$