Question

When comparing the f(x) = –x2 + 2x and g(x) = log(2x + 1), on which interval are both functions positive? (–∞, 0) (0, 2) (2, ∞) (–∞, ∞)

Answer 1

X=0 positivo, is the answers

Answer 2

To compare the two functions, it is necessary to find the x values for which each function is positive.

For f(x), we can solve for when it is positive by setting the equation equal to zero and finding the x-intercepts.

-x^2 + 2x = 0

-x(x - 2) = 0

-x = 0 and x = 2

This tells us that f(x) is positive for (-inf, 0) and (2, inf).

Next, for g(x), we can solve for when it is positive by setting the equation equal to zero and finding the x-intercept.

log(2x+1) = 0

2x + 1 = 1

x = 0

This tells us that g(x) is positive for (0, inf).

Therefore, the interval on which both functions are positive is (0, 2).