Question

given the function, $f(x)=(x - 4)^3 + 1$, the root of the function is $x=$ type your answer...

Explanation:

Step1: Set function equal to 0

$f(x) = 0 \implies (x-4)^2 + 1 = 0$

Step2: Isolate the squared term

$(x-4)^2 = -1$

Step3: Solve for $x$ using square roots

$x-4 = \pm\sqrt{-1} = \pm i$

Step4: Solve for $x$

$x = 4 \pm i$

Answer:

$x=4+i$ and $x=4-i$