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

Answer:

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

Explanation:

Step1: Find $(f + g)(x)$

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

Step2: Recall the property of absolute - value

The absolute - value function $y = |x|$ has the property that $|x|\geq0$ for all real values of $x$.

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

If $|x|\geq0$, then $|x| + 3\geq0 + 3$. So, $(f + g)(x)\geq3$ for all values of $x$.