The value of f(x) = 4(2)x.
Point (1, 8): In this function, f(1) = 4(2)^1 = 8, which matches the given value.
Point (4, 64): f(4) = 4(2)^4 = 64, again matching the given value.
Other options:
f(x) = 2(4)x: This would give f(1) = 8, but f(4) = 256, not 64.
f(x) = 4(2)−x: This would give f(1) = 2, not 8, and f(4) = 0.5, not 64.
f(x) = 2(4)−x: Similar to the previous option, this would not match both points.
Therefore, f(x) = 4(2)x is the only function that passes through both given points, making it the correct exponential function.