Question

Find the inverse of P(x)=-15x^2+350x-2000 and state it’s domain.

Answer 1

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

$y = \sqrt{\frac{x+4042.14}{15}}-11.67$

$f^{-1}(x) = \sqrt{\frac{x+4042.14}{15}}-11.67$

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