Question

If f(x)=6x+3, find f⁻¹(x).
a) f⁻¹(x)=3−6x
b) f⁻¹ (2)=15
c) f⁻¹(2)=6x+3
d) f′-2

Answer 1

The inverse function of f(x)=6x+3 is f-1(x)=(x-3)/6, and evaluating f-1(2) yields -1/6, which is not provided as an option in the student's list.

Step-by-step explanation:

Finding the Inverse Function f-1(x)

To find the inverse of the function f(x)=6x+3, we follow certain steps. First, we replace f(x) with y:

y = 6x + 3

Next, we swap x and y to make y the subject of the equation:

x = 6y + 3

Then, we solve for y:

• Subtract 3 from both sides: x - 3 = 6y
• Divide both sides by 6: f-1(x) = (x - 3) / 6

So the inverse function is f-1(x) = (x - 3) / 6. Now, let's evaluate f-1(2):

f-1(2) = (2 - 3) / 6 = -1 / 6

The correct answer is not listed as an option provided by the student.