A pupil posted this query to Reddit AskMath.
f(x) = 9 – √x
g(x) = 4x2
Discover the values for which f(g(x)) < 0
The scholar discovered the reply as x > 4.5 and x < -4.5, however the instructor mentioned it ought to solely be x > 4.5. Who’s appropriate?
As regular, watch the video for an answer.
Who is correct: me or my instructor?
Or preserve studying.
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“All will probably be nicely for those who use your thoughts on your choices, and thoughts solely your choices.” Since 2007, I’ve devoted my life to sharing the enjoyment of recreation principle and arithmetic. MindYourDecisions now has over 1,000 free articles with no advertisements due to group help! Assist out and get early entry to posts with a pledge on Patreon.
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Reply To Who is correct: me or my instructor?
(Just about all posts are transcribed shortly after I make the movies for them–please let me know if there are any typos/errors and I’ll appropriate them, thanks).
f(x) = 9 – √x
g(x) = 4x2
Discover the values for which f(g(x)) < 0
f(g(x))
= f(4x2)
= 9 – √(4x2)
= 9 – √((2x)2)
= 9 – |2x|
We are able to break up absolutely the worth into two circumstances.
2x > 0
9 – 2x < 0
9 < 2x
4.5 < x
2x < 0
9 – (-2x) < 0
9 + 2x < 0
2x < -9
x < -4.5
The scholar is appropriate. It seems the instructor was proscribing the area of f(x) to non-negative values, as can be the case for 9 – √x. However once we first apply the perform g, we then have 9 – √(4x2) which has a domian of all actual numbers.
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Reference
Reddit AskMath
https://www.reddit.com/r/askmath/feedback/1kxu28g/who_is_right_me_or_my_teacher/
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