Question 11

Explanation

Given the equation $(f(x))^2 - 6f(x) = -8$ with $f(x) = 2x - 4$.

First, we rewrite the equation into the general form of a quadratic equation:

Then we substitute $f(x) = 2x - 4$ into the equation:

Expand the quadratic form and simplify the equation:

From the quadratic equation $ax^2 + bx + c = 0$, the product of the roots ($x_1 \cdot x_2$) is given by the formula $\frac{c}{a}$.

Given:

$a = 4$ $b = -28$ $c = 48$

Then:

So, the value of $x_1 \cdot x_2$ is $12$.