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Q.16
Given f (x) = x2 + 2x – 5 and values of the linear function g(x) in the table, what is the range of (f + g)(x)?


x –6 –3 –1 4
g(x) 16 10 6 –4

A. (–∞, –1]
B. [–1, ∞)
C. [–1, 1]
D. ℝ

1 Answer

2 votes

To find the range of the function (f + g)(x), we need to evaluate the sum of f(x) and g(x) for each corresponding x-value in the table.

Let's first calculate the values of f(x) + g(x) using the given values:

For x = -6:

(f + g)(-6) = f(-6) + g(-6) = (-6)^2 + 2(-6) - 5 + 16 = 36 - 12 - 5 + 16 = 35

For x = -3:

(f + g)(-3) = f(-3) + g(-3) = (-3)^2 + 2(-3) - 5 + 10 = 9 - 6 - 5 + 10 = 8

For x = -1:

(f + g)(-1) = f(-1) + g(-1) = (-1)^2 + 2(-1) - 5 + 6 = 1 - 2 - 5 + 6 = 0

For x = 4:

(f + g)(4) = f(4) + g(4) = (4)^2 + 2(4) - 5 - 4 = 16 + 8 - 5 - 4 = 15

Now, let's examine the calculated values:

(f + g)(-6) = 35

(f + g)(-3) = 8

(f + g)(-1) = 0

(f + g)(4) = 15

The range of (f + g)(x) is the set of all possible output values. Looking at the calculated values, we can see that the range includes 35, 8, 0, and 15. Therefore, the range is:

Range = {35, 8, 0, 15}

None of the given answer choices precisely matches this range. However, option D. ℝ represents the set of all real numbers, which encompasses the range {35, 8, 0, 15}. Therefore, the closest answer choice is D. ℝ.

User Denise Mauldin
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