Question

Algebraically determine the inverse of the function f(x)= 12x2+5.

Answer 1

Answer:

Step-by-step explanation:

f(x)= 12x2+5 should be written as  f(x) = 12x^2 + 5; the " ^ " symbol signifies exponentiation and is mandatory.

Here's how we find the inverse function.

1.  Apply the horizontal line test.  if a horizontal line intersects the graph in more than one place, the function is not one-to-one and does not have an inverse for all x.  However, if we focus on only [0, infinity), this part of the graph does have an inverse, which we can find as follows:

2.  Replace 'f(x)' with 'y:  y = 12x^2 + 5

3.  Interchange x and y:  x = 12y^2 + 5

                                                              x - 5

4.  Solve for y:  12y^2 = x - 5;   y^2 = ------------

                                                                12

                          x - 5

               y = √(----------)

                             12