Answer: The inverse of f(x) is not a function because it does not satisfies the vertical line test.
Explanation:
The given function is,
[tex]f(x)=(7-8x)^2[/tex]
[tex]y=(7-8x)^2[/tex]
Interchange the variables and find the value of y to determine the inverse of f(x).
[tex]x=(7-8y)^2[/tex]
[tex]\pm \sqrt{x}=7-8y[/tex]
[tex]y=\frac{7\pm \sqrt{x}}{8}[/tex]
put [tex]y=f^{-1}(x)[/tex]
[tex]f^{-1}(x)=\frac{7\pm \sqrt{x}}{8}[/tex]
For each value of x there are two values, so it will not satisfy the vertical line test.
According to vertical line test the graph of a function intersect the vertical line at most once. It means for each x there exist a unique value of y.
Since the [tex]y=f^{-1}(x)[/tex], does not satisfy the vertical lines test, therefore the inverse of given function is not a function.
