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.

Question
Composite functions
asked 2021-03-09
Given that
\(\displaystyle{f{{\left({x},{y},{z}\right)}}}={x}{y}+{z},\)
\(\displaystyle{x}={s}^{{2}},\)
\(\displaystyle{y}={s}{t},\)
\(\displaystyle{z}={t}^{{2}},\)
find the composite function.

Answers (1)

2021-03-10
\(\displaystyle{f{{\left({x},{y},{z}\right)}}}={x}{y}+{z}\)
Substitute \(\displaystyle{x}={s}^{{2}}\), \(\displaystyle{y}={s}{t}\), and \(\displaystyle{z}={t}^{{2}}\)
\(\displaystyle{f{{\left({x},{y},{z}\right)}}}={\left({s}^{{2}}\right)}{\left({s}{t}\right)}+{t}^{{2}}\)
\(\displaystyle{f{{\left({x},{y},{z}\right)}}}={\left({s}^{{2}}\cdot{s}^{{1}}{t}\right)}+{t}^{{2}}\)
\(\displaystyle{f{{\left({x},{y},{z}\right)}}}={\left({s}^{{2}}+{1}\cdot{t}\right)}+{t}^{{2}}\) [because \(\displaystyle{a}^{{n}}\cdot{a}^{{m}}={a}^{{{n}+{m}}}\)]
\(\displaystyle{f{{\left({x},{y},{z}\right)}}}={s}^{{3}}{t}+{t}^{{2}}\)
0

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