Answer:
Range of the function f(x) = 3x² +18x is [-27,∞).What is the range of a function?The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.Here, we have f(x) = 3x² +18x.Let f(x) = y⇒ y = 3x² +18x⇒ y = 3(x²+6x)⇒ y/3 = x²+6x⇒ y/3 = x²+ 6x + 9 - 9⇒ y/3 = (x+3)² - 9⇒ y/3 + 9 = (x+3)² ⇒ (y+27)/3 = (x+3)² Taking square root on both sides, we get⇒ = x+ 3⇒ = xNow since f(x) = y ⇒ x = f⁻¹(y)⇒ f⁻¹(y) = ⇒ range = [-27,∞).Therefore, range of the function f(x) = 3x² +18x was found to be [-27,∞).
Explanation: