Question

What is the inverse of f(x)=x^4+7 for x>0 where function g is the inverse of function f? -

Answer 1

Answer:

$g(x) = \sqrt[4]{x-7},~ x\geq 7$

Step by step explanation:

$y= f(x) = x^4+7\\\\\text{Replace x with y and solve for y:}\\\\~~~~~~~x = y^4 +7\\\\\implies y^4 = x-7\\\\\implies y = \pm\sqrt[4]{x-7}\\\\ \implies f^{-1}(x) = \pm\sqrt[4]{x-7}$