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Let R be the region bounded by the functions f(x)=-3ˣ²+8 and g(x)=4ˣ²

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Final answer:

To find the region bounded by the functions f(x) = -3ˣ² + 8 and g(x) = 4ˣ², set the two equations equal to each other and solve for x. The region is bound by the x-values -√(8/7) and √(8/7).

Step-by-step explanation:

To find the region bounded by the functions f(x) = -3ˣ² + 8 and g(x) = 4ˣ², we need to identify the points where these two functions intersect. Set the two equations equal to each other and solve for x:

-3ˣ² + 8 = 4ˣ²

Combine like terms:

7ˣ² = 8

Divide both sides by 7:

ˣ² = 8/7

Take the square root of both sides:

ˣ = ±√(8/7)

So the region R is bound by the x-values -√(8/7) and √(8/7).

User Isuru Amarathunga
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