Question

Given the values of the linear functions f (x) and g(x) in the tables, where is (f – g)(x) positive? X -8 -5. -2. 1. 4. F(x) -4. -6 -8 -10 -12G(x) -14 -11 -8 -5 -2

Answer 1

Given:

The table of function is:

Find-:

Where (f-g)(x) is positive.

Explanation-:

The function of values is:

$(f-g)(x)=f(x)-g(x)$

The f(x)-g(x) value is:

$\begin{gathered} f(x)-g(x)=f(-8)-g(-8) \\ \\ =-4-(-14)=\text{ Positive} \\ \\ f(-5)-g(-5) \\ \\ =-6-(-11)=\text{ Positive} \\ \\ f(-2)-g(-2)=-8-(-8) \end{gathered}$

So positive interval for (f-g)(x)

$\begin{gathered} (f-g)(x)=\text{ Positive interval } \\ \\ (-\infty,-2) \end{gathered}$

The positive interval for function ( f - g )( x ) is (-∞, -2)