The inequality f(x) > g(x) holds for all x > a when f(x) = 2x and g(x) = x^2. To find when f(x) is always greater than g(x), we need to solve the inequality:
2x > x^2
Rearranging to standard form:
x^2 - 2x < 0
Factoring:
x(x - 2) < 0
The critical points are x = 0 and x = 2. We need to determine when the inequality holds true for x > a.
For x > 2, both x and (x-2) are positive, so the inequality is satisfied.
Therefore, f(x) = 2x is always greater than g(x) = x^2 for all x > 2.
At what point a
is f(x)=2x
always greater than g(x)=x2
for all x>a
(1 point)
1 answer