Given that f(x, y, z) = xy + z, x = s^2, y = st, z = t^2, find the composite function.

Given that f(x, y, z) = xy + z, x = s^2, y = st, z = t^2, find the composite function.

Composite functions
asked 2021-03-09
Given that
find the composite function.

Answers (1)

Substitute \(\displaystyle{x}={s}^{{2}}\), \(\displaystyle{y}={s}{t}\), and \(\displaystyle{z}={t}^{{2}}\)
\(\displaystyle{f{{\left({x},{y},{z}\right)}}}={\left({s}^{{2}}+{1}\cdot{t}\right)}+{t}^{{2}}\) [because \(\displaystyle{a}^{{n}}\cdot{a}^{{m}}={a}^{{{n}+{m}}}\)]

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