Question

Can someone give me a decent explanation on how you came up with your answer. Thanks!

Answer 1

the correct option is C.

Explanation:

The x-intercept of both functions g(x) and f(x) occur at point (1, 0).

Now, we need to find where g(x) > f(x) and f(x) > g(x)

We know that the greater the base of a logaritmic function is, the faster it will grow/decay.

For that reason, we can say that g(x) > f(x) on (1, +inf).

Now, when x<1 then y<0. So on the interval (0, 1) the function g(x) will decay much faster than the function f(x), so we can say that f(x) > g(x) on (0, 1). So the correct option is C.

Check the graph, to verify all this.