Question 7

Explanation

We are given the equation $(f(x))^2 = 5f(x) - 4$. We can rearrange it into a quadratic equation in terms of $f(x)$:

This equation is satisfied by $x_1$ and $x_2$. Based on the sum of roots formula for quadratic equations ($x_1 + x_2 = -\frac{b}{a}$), the sum of the values of $f(x)$ satisfying the equation is:

Given $f(x) = x + 1$. We substitute this into the equation above:

Thus, the value of $x_1 + x_2$ is $3$.