A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output...

4 0

3 years ago

Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] y = ta

Irina-Kira [14]

Answer:

The inner function is $u = \pi x$ .

The outer function is $f(u) = \tan{u}$ .

$\frac{dy}{dx} = y^{\prime} = \sec^{2}(u)*\pi = \pi\sec^{2}{\pi x}$

Step-by-step explanation:

The inner function is the one we apply the outer function to.

$y = \tan{\pi x}$

We apply the outer function tangent to $\pi x$ .

So, the inner function is $u = \pi x$ .

The outer function is $f(u) = \tan{u}$ .

The derivative of a compositve function

$y = f(u)$ in which $u = g(x)$ is given by the following function.

$y^{\prime} = f^{\prime}(u)*g^{\prime}(x)$

$f(u) = \tan{u}$

$f^{\prime}(u) = \sec^{2}{u}$

$u = g(x) = \pi x$

$g^{\prime}(x) = \pi$

$y^{\prime} = f^{\prime}(u)*g^{\prime}(x)$

$\frac{dy}{dx} = y^{\prime} = \sec^{2}(u)*\pi = \pi\sec^{2}{\pi x}$

7 0

2 years ago

HELP PLS - QUIZ AND IM VERY CONFUSED

Katarina [22]

Ms Girl we on the Same Note tbh

5 0

2 years ago

The two functions below are used to represent the height of a rocket above the ground after it is launched. Which rocket reaches

Korvikt [17]

Answer:

Rocket B reaches a maximum height that is greater than the maximum height of Rocket A.

Step-by-step explanation:

A graph quickly shows the answer to this question.

In vertex form, the equation for Rocket A is ...

y = -6(x² -16x +8²) +6(8²)

y = -6(x -8)² +384 . . . . . . . . . maximum height is 384 feet

The corresponding equation for Rocket B is ...

y = -4(x² -20x +10²) +4(10²)

y = -4(x -10)² +400 . . . . . . . . maximum height is 400 feet

Rocket B reaches a maximum height greater than that of Rocket A.

7 0

2 years ago

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