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).