Question

If f(x) = 1x1 + 9 and g(x) = -6, which describes the value of (f + g)(x)?

(f + g)(x) > 3 for all values of x
(f + g)(x) < 3 for all values of x
(f + g)(x) < 6 for all values of x
(f + g)(x) 6 for all values of x
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Answer 1

The answers are "(f+g)(x)> 3 for all values of x" and "(f+g)(x)<6 for all values of x".

Explanation:

• If f(x) = 1x1 + 9 =10, then f(x) is a constant for every value of x, which means that y=f(x) will take the value of 10 no matter which value takes x.
• If g(x)= -6, then g(x) is a constant for every value of x, which means that it will take the value of -6 no matter the value of x.
• (f+g)(x)=10 + (-6) = 10 - 6= 4. Then, no matter the value of x, the function (f+g)(x) will equal 4 (a constant).

• According to the available options, both "(f+g)(x)>3" and "(f+g)(x)<6" are true, because (f+g)(x)=4>3 and (f+g)(x)=4 <6.