The function f(x) = (x² + x + 1)/(x² - x + 1) is defined for every real x, because its denominator is never zero. Which of the following is the range of f, the set of all values it takes?

MathematicsMediumHigh School (11–12)Functions and Calculus › Graphs of Functions JEE Main

The function $f(x) = \dfrac{x^2 + x + 1}{x^2 - x + 1}$ is defined for every real $x$ , because its denominator is never zero. Which of the following is the range of $f$ , the set of all values it takes?

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← Let f(x) = 2x + 3 and g(x) = x² - 1 be functions from the real numbers to the real numbers. What is the sum of all real numbers x for which (f ° g)(x) = (g ° f)(x)?A function f from {1, 2, 3, 4} to {1, 2, 3} gives each of the numbers 1, 2, 3 and 4 a value 1, 2 or 3. For how many such functions is f(1) + f(2) + f(3) + f(4) = 8? Two functions are different when they differ at even one point. →

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