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Find g(x), where g(x) is the reflection across the x-axis of f(x)=x2–1.g(x)=x2–1g(x)=–x2–1g(x)=–x2+1g(x)=x2+1Submit

Question

Find g(x), where g(x) is the reflection across the x-axis of f(x)=x2–1.g(x)=x2–1g(x)=–x2–1g(x)=–x2+1g(x)=x2+1Submit

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Solution

The reflection of a function across the x-axis is found by changing the sign of the y-values. In this case, the function f(x) = x^2 - 1 becomes g(x) = -(x^2 - 1) when reflected across the x-axis.

To simplify this, distribute the negative sign:

g(x) = -x^2 + 1

So, the function g(x) = -x^2 + 1 is the reflection of the function f(x) = x^2 - 1 across the x-axis.

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