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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) =​

Consider the given function. f(x) = e² - 4 To determine the inverse of the given function-example-1

1 Answer

1 vote

Answer:


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.

User Aea
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