Answer:
This method is incorrect.
Step-by-step explanation:
The student's understanding of an exponent -1 is correct, but applying it to the inverse function f^-1(x), is wrong.
The method to find inverse function is to replace f(x) with y, switch x and y, then solve for y.
To use the (incorrect) "simple method" Put a 1 on top and move the function to the bottom (denominator).
For example, let's look at the function f(x) = x+3
Write y in place of f(x).
y = x + 3
Switch x and y.
x = y + 3
Solve for y.
Subtract 3.
x - 3 = y
Rewrite.
y = x - 3
This is the proper inverse function.
f^-1 (x) = x - 3
Using the (incorrect) "simple method"
f(x) = x + 3
f^-1(x) = 1/(x+3)
This shows that the shortcut doesnot work, its wrong. To do it correctly, switch x and y and solve for y.
