Question

Which of the following is true with respect to the following functions:f(x) - 3x + 141 g(x) = x4 +3x2 - 14h(x) - 3* +1(x) = log2 (x + 1)-A. The domains of g(x) and h(x) include all real numbers while thedomains of (x) and h(x) are restricted.B. i(x) and h(x) are inverse functions.C. (x) increases the most rapidly.D. The range of f(x) includes lesser (more negative) y-values than theranges of f(x), g(x), or h(x).

Answer 1

To identify which of the following options are true:

Option 1: Yes, the domains of g(X) and h(x) include all real numbers but since it says h(x) is restricted, Option 1 is not true.

Option 2: The function i(x) and h(x) are not inverse function because the inverse of log₃ (x + 1) is 3^x - 1. Option 2 is not true as well.

Option 3: Out of the 4 functions, i(x) is not the function that increases most rapidly. Hence, Option 3 is not true as well.

Option 4: The range of f(x) is y ≥ 0. The range of g(x) is y ≥ - 14. The range of h(x) is y > 1. The range of i(x) is all real numbers. Hence, the range of i(x) includes more negative y-values than the ranges of f(x), g(x), or h(x). Option 4 is true.