Step 1 :To find the inverse of the function \(f(x)=4x^3-3\), we first replace \(f(x)\) with \(y\), so the equation becomes \(y=4x^3-3\).
Step 2 :Next, we swap \(x\) and \(y\) to get \(x=4y^3-3\).
Step 3 :Then, we solve for \(y\) to get the inverse function. Add 3 to both sides to get \(x+3=4y^3\).
Step 4 :Divide both sides by 4 to get \(\frac{x+3}{4}=y^3\).
Step 5 :Finally, take the cube root of both sides to get \(y=\sqrt[3]{\frac{x+3}{4}}\).
Step 6 :So, the inverse function is \(f^{-1}(x)=\sqrt[3]{\frac{x+3}{4}}\), which corresponds to option B.