Answer:
Not a function. The inverse is
[tex]y = \sqrt{ \frac{x + 5}{2} } [/tex]
and
[tex]y = - \sqrt{ \frac{x + 5}{2} } [/tex]
Step-by-step explanation:
Any even-degree polynomial functions that are inverted will not be a function.
[tex]f(x) = 2 {x}^{2} - 5[/tex]
Let y = f(x)
[tex] y = 2 {x}^{2} - 5[/tex]
To proceed the inverse, swap the x-term and y-term.
[tex]x = 2 {y}^{2} - 5[/tex]
Convert into function form.
[tex]x + 5 = 2 {y}^{2} \\ 2 {y}^{2} = x + 5 \\ {y}^{2} = \frac{x +5 }{2} [/tex]
The reason why inverted even-degree polynomial function cannot be a function because the inverse graph doesn't pass line test.
Thus the answer is
[tex]y = \sqrt{ \frac{x + 5}{2} } \\ y = - \sqrt{ \frac{x + 5}{2} } [/tex]
