Question

1. let f be a decreasing function defined for x ≥ 0. the function g is given by g(x) = log₂x. (a) (i) the function h is defined by h(x) = (g ∘ f)(x) = g(f(x)). find the value of h(0), or indicate that it is not defined. (ii) find the value of f⁻¹(4), or indicate that it is not defined. (b) determine the end behavior of g as x increases without bound. express your answer using the mathematical notation of a limit. (c) (i) use the table of values of f(x) to determine if f is best modeled by a linear, quadratic, exponential, or logarithmic function. (ii) give a reason for your answer based on the relationship between the change in the output values of f and the change in the input values of f.

Explanation:

Answer:

3
1
\(\lim_{x
ightarrow\infty}g(x)=\infty\)
exponential
The output values over consecutive equal - length input - value intervals are proportional.