What is the range of the function ?
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Is the answer E? I got that by plugging in x=2 and seeing g(2)=1, and since the square root only makes the value smaller from there, the output can't exceed 1.
That's the way I did it too — the minus in front of the root is what caps it.
Yeah but does the domain matter for the range here? I always get tripped up on that.
Took me a second to remember that sqrt(x-2) is always non-negative, so 1 minus something non-negative can never be bigger than 1. Once I saw that it clicked.
This is the key insight. The range is basically driven by the sign of that square root term.
I initially picked A because I was thinking about the minimum value, but the question asks for range and I overthought the lower bound. Tricky wording.
Same trap here. The lower bound isn't bounded because x can grow forever, so the function keeps decreasing.
Solid 605-655 level question. Not hard conceptually but the answer choices are designed to catch people who only check one endpoint.
What it tests
Your ability to evaluate and compose functions, including unusual defined operations.
Common trap
Applying function operations in the wrong order or ignoring domain restrictions.