Mathematics

Problem

(a) Explain what is meant by a composite function and illustrate your explanation with one example that is NOT the same as the one given in your textbook. (b) For the function

y = \sqrt{5x^{4}+2}

, (i) clearly identify an “inner” function

u(x)

and an “outer” function

f(u)

so that

y = f\bigl(u(x)\bigr)

, (ii) write

y

in the form

f(u)

using the functions you have chosen in part (i). (c) Using your identification from part (b), find

\displaystyle \frac{dy}{dx}

and simplify your final answer as far as possible. (i) clearly identify an “inner” function

u(x)

and an “outer” function

f(u)

so that

y = f\bigl(u(x)\bigr)

, (ii) write

y

in the form

f(u)

using the functions you have chosen in part (i).

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