Question

Consider the following functions.

[f(x) = 2ˣ/2]
[g(x) = √x - 3]

Find the value of the following function: ((g + f)(x) = (aˣ + x - b)¹/2)

Options:
a) (2ˣ), (3)
b) (x), (2ˣ)
c) (√x), (3)
d) (2√x), (3)

Answer 1

The correct value for the function (g + f)(x) expressed as ( aˣ + x - b)^1/2 is obtained by summing the given functions f(x) and g(x). The function (g + f)(x) simplifies to (2ˣ + √x - 3). The answer matches option (a), which presents 'a' as 2ˣ and 'b' as 3.

Step-by-step explanation:

The student is asked to find the value of the function (g + f)(x), which is expressed as ( aˣ + x - b)^1/2. We are given the functions f(x) = 2ˣ/2 and g(x) = √x - 3. The sum of these functions, (g + f)(x), is therefore (√x - 3 + 2ˣ/2). To find the correct expression for this sum, we must match this to the given expression of the combined function, ( aˣ + x - b)^1/2, and identify the correct values for 'a' and 'b' in the options provided. The correct match is option (a) (2ˣ), (3) because 2ˣ/2 simplifies to 2ˣ, and √x - 3 matches the format x - b, where b equals 3.