Find the inverse of:
[tex]f(x)=(x+3)^2[/tex]
a. To sketch f(x), we use the graph of the parent function
[tex]g(x)=x^2[/tex]
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:
[tex]y=(x+3)^2[/tex]
Applying square root on both sides:
[tex]\pm\sqrt{y}=x+3[/tex]
Solving for x:
[tex]x=\pm\sqrt{y}-3[/tex]
Swapping letters:
[tex]y=\pm\sqrt{x}-3[/tex]
Since we have chosen only the non-negative part of the domain for f(x), we use only the positive sign:
[tex]f^{-1}(x)=\sqrt{x}-3[/tex]
Both functions, f(x) and its inverse are shown below:
