Find the inverse of:
[tex]f(x)=(3x-24)^2[/tex]
The variable x can take any real value and the function f(x) exists. This means
the domain of f(x) is (-∞, +∞).
Now find the inverse function.
[tex]\begin{gathered} y=(3x-24)^2 \\ \pm\sqrt[]{y}=3x-24 \\ \pm\sqrt[]{y}+24=3x \\ x=\frac{\pm\sqrt[]{y}+24}{3} \\ x=\pm\frac{1}{3}\sqrt[]{y}+8 \end{gathered}[/tex]
Swapping letters, we get the inverse function:
[tex]y=\pm\frac{1}{3}\sqrt[]{x}+8[/tex]
For each value of x, we get two values of y, thus this is not a function.
The domain of the inverse is restricted to values of x that make the square root exist, thus the domain is x ≥ 0, or [0, +∞)
The range of the inverse is the domain of the original function, that is, (-∞, +∞)
Function: No
Domain: [0, +∞)
Range: (-∞, +∞)
The choice to select is shown below.
