Tutor profile: Claudia J.
How to determine if a function has an inverse function?
A function has an inverse function if it is one to one. For example, f(x) = 5x+3 has an inverse function, because one x value corresponds to one f(x) value However, g(x) = x^2 does not have an inverse function. Because two x values can lead to the same g(x) value. For example: x = 2 or x = -2 you will get g(x) = 4 for both values of x
How do you find the maximum or minimum of a quadratic equation?
Take the first derivative of the equation and set it = 0. Explanation: By taking the first derivative of the equation, you get the slope of the corresponding curve. You want to find the highest/lowest point of the parabola, which is flat, hence we set the slope = 0.
How do you decide how many real solution a quadratic equation has?
Use discriminant. Formula: b^2 + 4*ac, where the quadratic equation is written in the general form (ax^2+bx+c=0) Explanation: This formula is part of the quadratic formula. If it's negative, we know the equation has no real solution, as it is impossible to take square root of a negative number. If it's positive, we know the equation has two real solutions, as it will be -b/2a minus or add a number If it is = 0, the equation has one real solution. as the answer will simply just be -b/2a
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