Exercise | Wiskunde op Tilburg University

Consider the function

$y(x) = 2^{5x^2+3}$ . Is this a composite function? If so, how can you choose

$v(x)$ and

$u(v)$ in a convenient way?

Antwoord 1 correct

Correct

Antwoord 2 optie

$y(x)$ is a composite function consisting of

$v(x) = x^2$ and

$u(v) = 2^{5v+3}$ .

Antwoord 2 correct

Fout

Antwoord 3 optie

$y(x)$ is a composite function consisting of

$v(x) = 5x^2$ and

$u(v) = 2^{v+3}$ .

Antwoord 3 correct

Fout

Antwoord 4 optie

$y(x)$ is not a compostite function, because

$y(x)$ cannot be written as

$u(v(x))$ .

Antwoord 4 correct

Fout

Antwoord 1 optie

$y(x)$ is a composite function consisting of

$v(x) = 5x^2+3$ and

$u(v) = 2^v$ .

Antwoord 1 feedback

Correct: It holds that

$u(v(x)) = 2^{v(x)} = 2^{5x^2+3} = y(x)$
and moreover,

$v(x)$ and

$u(v)$ can be differentiated by the use of Derivatives elementary functions and the Rules of differentiation.

Go on.

Antwoord 2 feedback

Wrong:

$y(x)$ is indeed a composite function and

$y(x) = u(v(x))$ , but

Antwoord 3 feedback

Wrong:

$y(x)$ is indeed a composite function and

$y(x) = u(v(x))$ , but

Antwoord 4 feedback

Wrong:

$y(x)$ is a composite function. (Every function can be written as

$u(v(x))$ .)

See Composite function.