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}}

Step 1:

Switch f(x) for y, 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 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: ${\begin{array}{rcl}x&=&{\frac {3y}{2y-1}}\\x(2y-1)&=&3y\\2xy-x&=&3y\\2xy-3y&=&x\\y(2x-3)&=&x\\y&=&{\frac {x}{2x-3}}\end{array}}$

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}}