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vampirchik [111]
2 years ago
15

Trying to determine function of g(x).

Mathematics
2 answers:
Orlov [11]2 years ago
6 0

Answer:

g(x)=4\sqrt[3]{x}

Step-by-step explanation:

We can see that the curve has not been translated horizontally or vertically, nor has it been reflected in either axis.  Therefore, g(x) is a stretch:

y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis by a factor of}\:a

y=f(a x) \implies f(x) \: \textsf{stretched parallel to the x-axis by a factor of} \: \dfrac{1}{a}

Parent function f(x)=\sqrt[3]{x}

\implies g(x)=a\:f(x)=a\sqrt[3]{x}

\textsf{or}\quad g(x)=f(ax)=\sqrt[3]{ax}

From inspection of the graph:

g(1)=4

Therefore:

\implies a\sqrt[3]{1}=4

\implies a=4

\implies g(x)=4\sqrt[3]{x}

Or:

\implies \sqrt[3]{a(1)}=4

\implies a=4^3

\implies a=64

\implies g(x)=\sqrt[3]{64x}

\implies g(x)=\sqrt[3]{64}\sqrt[3]{x}

\implies g(x)=4\sqrt[3]{x}

Therefore, the translated function is:

g(x)=4\sqrt[3]{x}

mario62 [17]2 years ago
3 0

Answer:

To find f(g(x)), we just substitute x = g(x) in the function f(x). For example, when f(x) = x2 and g(x) = 3x - 5, then f(g(x)) = f(3x - 5) = (3x - 5)2.

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