If f of x is equal to absolute value of x plus 9 and g of x is equal to negative 6 , which describes the range of open paren f plus g close paren of x ?
Answer
A
open paren f plus g close paren of x is less than or equal to 6 for all values of x
B
open paren f plus g close paren of x is greater than or equal to 3 for all values of x
C
open paren f plus g close paren of x is less than or equal to 3 for all values of x
D
open paren f plus g close paren of x is greater than or equal to 6 for all values of x
Explanation
Add the functions: (f + g)(x) = |x| + 9 - 6 = |x| + 3. Since an absolute value is always at least 0, (f + g)(x) is always at least 3. Its range is therefore described by “greater than or equal to 3 for all values of x,” choice D.
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