Question

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

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Answer 1

`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}`