inverse functions

Question

Find the inverse function for each of the following: 

1)f(x)= x+9/3 

2)f(x)= - 16x-3/14

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find the inverse of each function, if it exists, state the domain and range for the original function and the inverse. 

1)f(x)=(x+2)²-5

2)f(x)=√x-3 

Answer 1

1. y = x + 9/3

x = y + 9/3

y = x - 9/3

f^-1(x) = x - 9/3

 

You do # 2.

 

1. y = (x + 2)² - 5

x = (y + 2)² - 5

x + 5 = (y + 2)²

√(x + 5) = y + 2

y = √(x + 5) - 2

f^-1(x) = √(x + 5) - 2

 

The domain and range of f(x) = all real numbers.

 

In the inverse, we can't take the square root of a negative number, so...

 

x + 5 ≥ 0

x ≥ -5

 

The range of f^-1(x) = all real numbers

 

You do # 2.