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09 Jan 2024, 09:37
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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80% (01:31) correct
20%
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If f(x) = g(x - 1), where g(x) = |x| + 1, which of the following must be true?
(A) f(x) < 0
(B) f(x) = 0
(C) f(x) > 0
(D) f(x) = 2
(E) f(x) = g(x)
Functions.png [ 24.92 KiB | Viewed 7580 times ]
(A) f(x) < 0
(B) f(x) = 0
(C) f(x) > 0
(D) f(x) = 2
(E) f(x) = g(x)
Attachment:
Functions.png [ 24.92 KiB | Viewed 7580 times ]
09 Jan 2024, 09:53
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callumdye
If f(x) = g(x-1), where g(x) = |x| + 1, which of the following must be true?
(A) f(x) < 0
(B) f(x) = 0
(C) f(x) > 0
(D) f(x) = 2
(E) f(x) = g(x)
(A) f(x) < 0
(B) f(x) = 0
(C) f(x) > 0
(D) f(x) = 2
(E) f(x) = g(x)
Since g(x) = |x| + 1, then f(x) = g(x - 1) = |x - 1| + 1 = (nonnegative value) + 1 = positive. Thus, f(x) > 0.
Answer: C.
General Discussion
09 Jan 2024, 12:13
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Bunnel soln is perfect but i did it longer way
If f(x) = g(x-1), where g(x) = |x| + 1, which of the following must be true?
Now
g(x-1)=|x-1|+1
If x-1>0 (implies x>1)
g(x-1)=x-1+1=x Always positive
if x-1<0 (implies x<1)
g(x-1) = -(x-1)+1
g(x-1) = 2 - x
This will again always be positive because all values of x<1
Hence f(x)=g(x-1)>0
f(x)>0
c
If f(x) = g(x-1), where g(x) = |x| + 1, which of the following must be true?
Now
g(x-1)=|x-1|+1
If x-1>0 (implies x>1)
g(x-1)=x-1+1=x Always positive
if x-1<0 (implies x<1)
g(x-1) = -(x-1)+1
g(x-1) = 2 - x
This will again always be positive because all values of x<1
Hence f(x)=g(x-1)>0
f(x)>0
c
