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MMLU-Pro / 7941 / Suppose f(x) is a function that has this property: For all real numbers a…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Suppose f(x)f(x) is a function that has this property: For all real numbers aa and bb such that a<ba<b, the portion of the graph of y=f(x)y=f(x) between x=ax=a and x=bx=b lies below the line segment whose endpoints are (a,f(a))(a,f(a)) and (b,f(b))(b,f(b)). (A function with this property is called strictly convex.) Given that f(x)f(x) passes through (−2,5)(-2,5) and (2,9)(2,9), what is the range of all possible values for f(1)f(1)? Express your answer in interval notation.
Plain-text mathematical notation (without MathML)
Suppose f(x) is a function that has this property: For all real numbers a and b such that a<b, the portion of the graph of y=f(x) between x=a and x=b lies below the line segment whose endpoints are (a,f(a)) and (b,f(b)). (A function with this property is called strictly convex.) Given that f(x) passes through (−2,5) and (2,9), what is the range of all possible values for f(1)? Express your answer in interval notation.
Original LaTeX notation
Suppose $f(x)$ is a function that has this property: For all real numbers $a$ and $b$ such that $a<b$, the portion of the graph of $y=f(x)$ between $x=a$ and $x=b$ lies below the line segment whose endpoints are $(a,f(a))$ and $(b,f(b))$. (A function with this property is called strictly convex.) Given that $f(x)$ passes through $(-2,5)$ and $(2,9)$, what is the range of all possible values for $f(1)$? Express your answer in interval notation.

category

math

options

  1. (-inf, 5)
  2. (-inf, 7)
  3. (-inf, 3)
  4. (-inf, 11)
  5. (-inf, 9)
  6. (-inf, 12)
  7. (-inf, 6)
  8. (-inf, 10)
  9. (-inf, 4)
  10. (-inf, 8)

src

ori_mmlu-high_school_mathematics

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Source and history

upstream_id / Original problem ID
7941
task_id
598266d7-3c62-5cdb-9993-151e3a92c2f9
task_key
default--test--7941
task_revision_id
1
config / split
default / test

Official source

initial import