Question

Consider the given function. f(x) = e² - 4 To determine the inverse of the given function, change f(x) to y, switch and y, and solve for In(x + The resulting function can be written as f-1(x) =​

Answer 1

`f^(-1)(x)=(\ln(x+4))/(2)`

Explanation:

`y=e^(2x)-4\\\\x=e^(2y)-4\\x+4=e^(2y)\\\ln(x+4)=2y\\(\ln(x+4))/(2)=y\\\\f^(-1)(x)=(\ln(x+4))/(2)`

Just swap x and y in the original function, and then solve for y to get the inverse function.