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Bunuel
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If f(a) = 6a – 4, and if the domain of a consists of all real numbers 11 Dec 2020, 11:15
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E
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87% (01:29) correct 13% (01:17) wrong based on 61 sessions

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If f(a) = 6a – 4, and if the domain of a consists of all real numbers defined by the inequality –6 < a < 4, then the range of f(a) contains all of the following members EXCEPT:

(A) –24
(B) \(\sqrt{\frac{1}{6}}\)
(C) 0
(D) 4
(E) 20
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E
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If f(a) = 6a – 4, and if the domain of a consists of all real numbers 11 Dec 2020, 11:21
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a=4, f(a)=20.
a<4, so (E)

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If f(a) = 6a – 4, and if the domain of a consists of all real numbers 12 Dec 2020, 05:42
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Bunuel
If f(a) = 6a – 4, and if the domain of a consists of all real numbers defined by the inequality –6 < a < 4, then the range of f(a) contains all of the following members EXCEPT:

(A) –24
(B) \(\sqrt{\frac{1}{6}}\)
(C) 0
(D) 4
(E) 20
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The domain is all values of \(a\) that satisfy the equation.

Here the inequality gives us the limits of \(a\).


The range is all the values of f(a) for which \(a\) is possible

Putting f(a) = -6, we get 6a - 4 = (6 * -6) - 4 = -40

Putting f(a) = 4, we get 6a - 4 = (6 * 4) - 4 = 20


So the range is defined as -40 < f(a) < 20

Running through the options, A, B C and D lie within the limits. E is not possible as f(a) < 20 and equal to 20.


Option E

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If f(a) = 6a – 4, and if the domain of a consists of all real numbers 14 Dec 2020, 04:29
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Bunuel
If f(a) = 6a – 4, and if the domain of a consists of all real numbers defined by the inequality –6 < a < 4, then the range of f(a) contains all of the following members EXCEPT:

(A) –24
(B) \(\sqrt{\frac{1}{6}}\)
(C) 0
(D) 4
(E) 20
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Solution:

We are given a linear function, and it is defined only on the interval -6 < a < 4. We want to find the largest and smallest values of f(a) because these values will determine the range of the function.Even though a < 4, the value of a can be as close to 4 as possible. So, if a were 4, we would have f(4) = 6(4) - 4 = 20. Similarly, on the other extreme, if a were -6, we would have f(-6) = 6(-6) - 4 = -40. In other words the range of f(a) is all values between -40 and 20, i.e., -40 < f(a) < 20. Since f(a) has to be strictly less than 20, we see that 20 can’t be a value in the range of the function.

Answer: E
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