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Hello, help me please )

Hello, help me please )-example-1

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Find the inverse of:


f(x)=(x+3)^2

a. To sketch f(x), we use the graph of the parent function


g(x)=x^2

Translated 3 units to the left:

b. The part of the function f(x) that is one-to-one and non-decreasing is in the domain [-3, ∞). Expressing in inequality notation: x ≥ -3.

c. The function f(x) can be written as:


y=(x+3)^2

Applying square root on both sides:


\pm√(y)=x+3

Solving for x:


x=\pm√(y)-3

Swapping letters:


y=\pm√(x)-3

Since we have chosen only the non-negative part of the domain for f(x), we use only the positive sign:


f^(-1)(x)=√(x)-3

Both functions, f(x) and its inverse are shown below:

Hello, help me please )-example-1
Hello, help me please )-example-2
User Andrew Kuklewicz
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