Answer:
The function given is:
P(x) = 15x² + 350x - 2000
or
y = 15x² + 350x - 2000
Interchange x and y:
x = 15y² + 350y - 2000
x = (y√15)² + 2(y√15)(45.19) + (45.19)² - (45.19)² - 2000
x = ( y√15 + 45.19)² - 4042.14
( y√15 + 45.19)² = x + 4042.14
Take square root:
y√15 + 45.19 = (√(x + 4042.14))
y√15 = (√(x + 4042.14)) - 45.19
[tex]y = \sqrt{\frac{x+4042.14}{15}}-11.67[/tex]
[tex]f^{-1}(x) = \sqrt{\frac{x+4042.14}{15}}-11.67[/tex]
The minimum value of x, for which function is defined and real, is x= -4042.14
Hence, the range of inverse is x ≥ -4042.14
