If g(x) = 2x + 3, what is the inverse of g(x)?

If g(x) = 2x + 3, what is the inverse of g(x)?

• A. x - 3/2
• B. ½ (x - 3)
• C. 3/2 + x
• D. 2x - 3

Answer: (B)

To find the inverse of the function g(x) = 2x + 3, we start by replacing g(x) with y: y = 2x + 3. To find the inverse, we need to solve for x in terms of y. We begin by isolating the term with x: y - 3 = 2x. Next, we divide both sides by 2 to solve for x: x = (y - 3) / 2. Now, we replace y with g⁻¹(x) (the notation for the inverse function) to express the inverse function in terms of x: g⁻¹(x) = (x - 3) / 2. Alternatively, this can be rewritten as: g⁻¹(x) = ½(x - 3). This form matches the correct answer. The other options do not correspond to the inverse function as derived. They either result from misapplying algebraic manipulations or incorrectly swapping variables without properly isolating the function. Thus, the inverse function of g(x) = 2x + 3, which is g⁻¹(x) = ½(x - 3), is indeed the correct choice.

To find the inverse of the function g(x) = 2x + 3, we start by replacing g(x) with y:

y = 2x + 3.

To find the inverse, we need to solve for x in terms of y. We begin by isolating the term with x:

y - 3 = 2x.

Next, we divide both sides by 2 to solve for x:

x = (y - 3) / 2.

Now, we replace y with g⁻¹(x) (the notation for the inverse function) to express the inverse function in terms of x:

g⁻¹(x) = (x - 3) / 2.

Alternatively, this can be rewritten as:

g⁻¹(x) = ½(x - 3).

This form matches the correct answer.

The other options do not correspond to the inverse function as derived. They either result from misapplying algebraic manipulations or incorrectly swapping variables without properly isolating the function. Thus, the inverse function of g(x) = 2x + 3, which is g⁻¹(x) = ½(x - 3), is indeed the correct choice.