Question

Hello, help me please )

Answer 1

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: