Question

55. Find the inverse function of $g(x)=\log _{4}\left(x^{3}+2\right)$ .

Answer 1

$y= g(x) = \log_4 (x^3 +2)\\\\\text{Replace x with y and solve for y:}\\\\~~~~x=\log_4 (y^3 +2)\\\\\implies y^3 +2 = 4^x\\\\\implies y^3 =4^x-2\\ \\\implies y = \sqrt[3]{4^x -2}\\\\\implies f^{-1} (x) = \sqrt[3]{4^x -2}$