if (f(x)=|x| + 9) and (g(x)=-6), which describes the range of ((f + g)(x))?\n((f + g)(x)geq3) for all values…

if (f(x)=|x| + 9) and (g(x)=-6), which describes the range of ((f + g)(x))?\n((f + g)(x)geq3) for all values of (x)\n((f + g)(x)leq3) for all values of (x)\n((f + g)(x)leq6) for all values of (x)\n((f + g)(x)geq6) for all values of (x)

if (f(x)=|x| + 9) and (g(x)=-6), which describes the range of ((f + g)(x))?\n((f + g)(x)geq3) for all values of (x)\n((f + g)(x)leq3) for all values of (x)\n((f + g)(x)leq6) for all values of (x)\n((f + g)(x)geq6) for all values of (x)

Answer

Explanation:

Step1: Find the expression for (f + g)(x)

$(f + g)(x)=f(x)+g(x)=|x| + 9+( - 6)=|x|+3$

Step2: Analyze the range of |x|

The absolute - value function $y = |x|$ has a range of $y\geq0$ for all real values of $x$.

Step3: Find the range of (f + g)(x)

If $y = |x|$ and $(f + g)(x)=y + 3$, then substituting the range of $y$ gives $(f + g)(x)\geq0 + 3$. So, $(f + g)(x)\geq3$ for all values of $x$.

Answer:

$(f + g)(x)\geq3$ for all values of $x$