If f(x)=x^3+3x^2-7. What is f⁻¹(-3)?
can someone explain how to get the answer. thanks.
Update:thanks but how do you solve that equation? Do you need to use the rational roots theorem or can it be solved an easier way?
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You must actually be looking for the solution to f(x) = -3.
x³ + 3x² - 7 = -3
x³ + 3x² - 4 = 0
Clearly 1 is a root, so factor out (x - 1).
(x - 1)(x² + 4x + 4) = 0
(x - 1)(x + 2)² = 0
x = 1, or x = -2
These solutions are not, however, f⁻¹(-3). The very fact that there is more than one solution proves that the function is not injective. It has no inverse.
f⁻¹(-3) => this is meaning inverse function. when y = -3, what is the x value?
-3 =x^3+3x^2-7
x^3+3x^2-4 = 0
solving
x = -2, 1