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f(x)=x^2. what is g(x)?

A. g(x)= 3x^2
B. g(x)= (1/3x)^2
C. g(x)= 1/3x^2
D. g(x)= 1/9x^2​

1 Answer

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Step-by-step explanation:

We want to get g(x) given that we know f(x) and the graphs for both functions. We will see that the correct option is D:

g(x) = (x/3)^2

By looking at the graph we can see that f(x) and g(x) are two quadratic functions, and g(x) is just a dilation of f(x).

This means that:

g(x) = A*f(x)

Where A is a real number.

We know that:

f(x) = x^2

And by looking at the graph, we also know that g(3) = 1.

Then we can write:

g(3) = A*f(3) = A*3^2 = 1

Now we can solve this for A:

A*3^2 = 1

A*9 = 1

A = 1/9

Then we have:

g(x) = (1/9)*f(x) = (1/9)*x^2 = (x/3)^2

So the correct option is D.

If you want to learn more about quadratic equations, you can read:

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