Beckett Henry
2022-09-12
Answered

A quantity $z$ is called a functional of $f(x)$ in the interval $[a,b]$ if it depends on all the values of $f(x)$ in $[a,b]$. What is the difference between a functional and a composite function?

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asked 2020-10-27

Decide whether the composite functions, $f\circ g$ and $g\circ f$ , are equal to x.

$f\left(x\right)={x}^{3}+9$

$g\left(x\right)=\sqrt[3]{x-9}$

asked 2021-03-09

Given that

$f(x,y,z)=xy+z,$

$x={s}^{2},$

$y=st,$

$z={t}^{2},$

find the composite function.

find the composite function.

asked 2022-09-09

Suppose you have a function $f$ such that

$$f(x)=a(b(c(d(x))))$$

Where $a$, $b$, $c$, and $d$ are all differentiable functions. Asked to find ${f}^{\prime}(x)$.

Can you "chain" the Chain Rule for $$4$$ functions and state that

$${f}^{\prime}(x)={a}^{\prime}(b(c(d(x))))\ast {b}^{\prime}(c(d(x)))\ast {c}^{\prime}(d(x))\ast {d}^{\prime}(x)$$

And even more generally, can you apply the same pattern for $n$ functions?

$$f(x)=a(b(c(d(x))))$$

Where $a$, $b$, $c$, and $d$ are all differentiable functions. Asked to find ${f}^{\prime}(x)$.

Can you "chain" the Chain Rule for $$4$$ functions and state that

$${f}^{\prime}(x)={a}^{\prime}(b(c(d(x))))\ast {b}^{\prime}(c(d(x)))\ast {c}^{\prime}(d(x))\ast {d}^{\prime}(x)$$

And even more generally, can you apply the same pattern for $n$ functions?

asked 2022-01-24

How do you write $y=\frac{1}{{x}^{2}+3}$ as a composition of two simpler functions?

asked 2021-09-09

Given

b.

asked 2021-05-28

Discuss the continuity of the function and evaluate the limit of f(x, y) (if it exists) as $(x,y)\to (0,0).f(x,y)={e}^{xy}$

asked 2021-01-31

Cameron stops to get gas soon after beginning a road trip. He checks his distance from home 2 hours after filling his gas tank and checks again 3 hours later. The first time he checked, he was 170 miles from home. The second time, he was 365 miles from home. What equation models Cameron's distance from home as a function of the time since getting gas?