# How do you find the first three iterate of the function f(x)=3x^2−4 for the given initial value x_0=1?

How do you find the first three iterate of the function $f\left(x\right)=3{x}^{2}-4$ for the given initial value ${x}_{0}=1$?
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coccusk7
Applying the function, we find:
${x}_{1}=f\left({x}_{0}\right)=3{x}_{0}^{2}-4=3{\left(1\right)}^{2}-4=3-4=-1$
${x}_{2}=f\left({x}_{1}\right)=3{x}_{1}^{2}-4=3{\left(-1\right)}^{2}-4=3-4=-1$
${x}_{3}=f\left({x}_{2}\right)=3{x}_{2}^{2}-4=3{\left(-1\right)}^{2}-4=3-4=-1$
In fact, for any $n\ge 1$ we have ${x}_{n}=-1$, since:
$f\left(-1\right)=3{\left(-1\right)}^{2}-4=-1$
is a fixed point.