Question

Two functions (f) and (g) are defined by (f: x + 2x^2 – 1) and (g: x + 3x + 2), where (x) is a real number.

(i) If (f(x - 1) – 7 = 0), find the values of (x).
a. (1)
b. (-1)
c. (2)
d. (-2)

Answer 1

To find the values of x, we substitute x - 1 into the function f, simplify to get a quadratic equation, and then solve for x using the quadratic formula or factoring, comparing the results with the given options.

Step-by-step explanation:

The student asked to find the values of x for the equation f(x - 1) – 7 = 0, given that f(x) = x + 2x2 – 1. First, we substitute (x - 1) into the function f, which leads to ((x - 1) + 2(x - 1)2 – 1). Simplifying this expression, we apply the distributive property and combine like terms to get a quadratic equation in the form ax2 + bx + c = 0. Then, this equation can be solved using the quadratic formula or factoring, if possible. After finding the values of x, we compare them with the provided options: a. (1) b. (-1) c. (2) d. (-2)