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For which of the following functions f(x), is it always true that f(a/

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Bunuel
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For which of the following functions f(x), is it always true that f(a/ [#permalink] New post   24 May 2021, 07:45
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A
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C
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E

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For which of the following functions f(x), is it always true that f(a/b) = f(b/a)?

A. f(x) = 1/x
B. f(x) = x^2
C. f(x) =1/(x/2)
D. f(x) = x+1
E. None of the above
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E
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For which of the following functions f(x), is it always true that f(a/ [#permalink] New post   24 May 2021, 07:51
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Asked: For which of the following functions f(x), is it always true that f(a/b) = f(b/a)?

A. f(x) = 1/x;
f(a/b) = b/a;
f(b/a)= a/b;
\(f(a/b) \neq f(b/a)\)

B. f(x) = x^2;
f(a/b) = (a/b)^2;
f(b/a)= (b/a)^2;
\(f(a/b) \neq f(b/a)\)

C. f(x) =1/(x/2) = 2/x;
f(a/b) = 2b/a;
f(b/a)= 2a/b;
\(f(a/b) \neq f(b/a)\)

D. f(x) = x+1;
f(a/b) = a/b + 1 = (a+b)/b ;
f(b/a)= b/a + 1 = (a+b)/a;
\(f(a/b) \neq f(b/a)\)
E. None of the above

IMO E
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Re: For which of the following functions f(x), is it always true that f(a/ [#permalink] New post   24 May 2021, 18:00
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Bunuel wrote:
For which of the following functions f(x), is it always true that f(a/b) = f(b/a)?

A. f(x) = 1/x
B. f(x) = x^2
C. f(x) =1/(x/2)
D. f(x) = x+1
E. None of the above


Let us try to plug in two values 2 and 0.5 in each answer, we must get the same result for it to be a candidate answer.

A: This only flips the x value. Incorrect.
B: This squares the x value so incorrect.
C: f(x) = 2/x, which is basically the same as choice A. Incorrect
D: Add 1 to the x value so incorrect.

Thus we choose E.

Ans: E
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Re: For which of the following functions f(x), is it always true that f(a/ [#permalink] New post   30 May 2021, 22:19
Expert Reply
To find
    • Among the option, for which function f(a/b) = f(b/a)
.

Approach and Working out:
f(a/b) = f(b/a)
    • If we replace a/b by x then b/a = 1/(a/b) = 1/x
      o Thus, f(x) = f(1/x)
    • Hence, we are looking for function that gives same value for x and 1/x.

Let’s check each option one by one.

    A. f(x) = \(\frac{1}{x}\)
      • F(\(\frac{1}{x}\)) = x.
      • F(x) ≠ F(\(\frac{1}{x}\))
      • This is incorrect.

    B. f(x) = \(x^2\)
      • F(\(\frac{1}{x}\)) = \(\frac{1}{x^2}\).
      • F(x) ≠ F(\(\frac{1}{x}\))
      • This is incorrect.

    C. f(x) =1/(x/2)
      • F(\(\frac{1}{x}\)) = \(\frac{1}{\frac{\frac{1}{x}}{2}}\). = \(\frac{2}{x}\)
      • F(x) ≠ F(\(\frac{1}{x}\))
      • This is incorrect.

    D. f(x) = x+1
      • F(\(\frac{1}{x}\)) = \(\frac{1}{x}\) + 1.
      • F(x) ≠ F(\(\frac{1}{x}\))
      • This is incorrect.

    E. None of the above
      • This option must be correct.

Hence, option E is the correct answer.
Correct Answer: Option E
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Re: For which of the following functions f(x), is it always true that f(a/ [#permalink] New post   08 Jun 2023, 15:14
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Re: For which of the following functions f(x), is it always true that f(a/ [#permalink]
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