Question

Table i contains outputs of the function f(x)=bˣ for some x values, and table ii contains outputs of the function g(x)= log_b(x) for some x values. In both functions, b is the same positive constant. What is the relationship between the outputs of the two functions?

1) The outputs of f(x) are always greater than the outputs of g(x)
2) The outputs of f(x) are always less than the outputs of g(x)
3) The outputs of f(x) are equal to the outputs of g(x)
4) The relationship between the outputs of f(x) and g(x) cannot be determined without knowing the specific values of x and b

Answer 1

The relationship between the outputs of the two functions is 1) The outputs of f(x) are always greater than the outputs of g(x)

What is the relationship between the outputs of the two functions?

From the question, we have the following parameters that can be used in our computation:

f(x) = bˣ

g(x) = logₙ(x)

Set b to a positive integer

Say b = 2

So, we have

f(x) = 2ˣ

g(x) = log₂(x)

The graph of the functions f(x) and g(x) is added as an attached

From the graph, we can see that the outputs of f(x) are always greater than the outputs of g(x)

This is true for other positive values of b

So, the true statement is (a)