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f(x) is a linear function such that, f(1) < f(2), f(3) > f(4) and f(5) = 25. What is the value of f(7)?  
  • a)
    49
  • b)
    0
  • c)
    25
  • d)
    Cannot be determined
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
f(x) is a linear function such that, f(1) <f(2), f(3) >f(4) and ...
Since f(x) is a linear function we can express f(x) as, f(x) = ax + b, where a and b are real numbers.
∴ f(1) < f(2)
a + b < 2a + b
∴ a > 0 ...(i)
∵ f(3) > f(4)
∴ 3a + b > 4a + b
∴ a < 0    ...(ii)
From (i) and (ii), we get a = 0
We know that f(5) = 25
∴ 5a + b = 25
Substituting the value of a in the above equation, we get b = 25 /(x) = 25, for all real numbers x. f(7) = 25 Hence, option 3.
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Most Upvoted Answer
f(x) is a linear function such that, f(1) <f(2), f(3) >f(4) and ...
And f(2) are known to be 5 and 8, respectively.
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