How do you find the inverse of y=x^2+12x?
1 Answer
Explanation:
The general steps to finding the inverse of a function are:
1 . Replacef(x) withy if it hasn't been done so already.
2 . Swapx andy .
3 . Solve fory .
4 . Replacey withf^-1(x) .
Using these four steps, let us find the inverse of
Starting with,
y=x^2+12x
Notice how
y=x^2+12x+(12/2)^2-(12/2)^2
y=(x+6)^2-(12/2)^2
y=(x+6)^2-36
Since the function is already denoted by the variable
x=(y+6)^2-36
Solving for
x+36=(y+6)^2
+-sqrt(x+36)=y+6
y=+-sqrt(x+36)-6
Replacing
color(green)( bar (ul ( | color(white)(a/a) color(black)(f^-1(x)=+-sqrt(x+36)-6) color(white)(a/a) | )))