Question

find f^-1(x) algebraically

Answer 1

\[f(x) =\frac{ 3 }{ 2x+1 }\]

Answer 2

First replace the notation f(x) with y:\[y = \frac{3}{2x+1}\]Next swap x and y everywhere in the function:\[x = \frac{3}{2y+1}\]Then use algebra to solve for y:\[(2y+1)x = 3\]\[2xy+x = 3\]\[2xy = 3-x\]\[y = \frac{3-x}{2x} = \frac{3}{2x} - \frac{1}{2}\]

Answer 3

thank you