005 Sample Final A, Question 4

Question Find the inverse of the following function Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x) = \frac{3x}{2x-1}}

Foundations:
1) How would you find the inverse for a simpler function like Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x) = 3x + 5} ?
Answer:
1) you would replace f(x) by y, switch x and y, and finally solve for y.

Step 1:

Switch f(x) for y, to get Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle y={\frac {3x}{2x-1}}} , then switch y and x to get Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x = \frac{3y}{2y-1}}

Step 2:

Now we have to solve for y: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{rcl} x & = & \frac{3y}{2y-1}\\ x(2y - 1) & = & 3y\\ 2xy - x & = & 3y\\ 2xy - 3y & = & x\\ y(2x - 3) & = & x\\ y & = & \frac{x}{2x - 3} \end{array}}

Final Answer:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y = \frac{x}{2x-3}}