Quantitative Aptitude – Algebra – Functions – If f(ab) = f(a)f(b) for all positive

Quantitative Aptitude – Algebra – Functions

Question

If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is

Answer

1

Solution

From CAT 2017 – Quantitative Aptitude – Algebra – Functions, we can see that,

Let us take the case when a=b=1
So, f(1) = f(1) f(1)
f(1) = [f(1)]^2
f(1)[f(1)-1] = 0
f(1) = 1
So, the maximum value of f(1) = 1
Answer: 1

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Algebra – Functions

Quantitative Aptitude – Algebra – Functions – Q1: Let f(x) = 2x-5 and g(x) = 7-2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if
Quantitative Aptitude – Algebra – Functions – Q2: Let f(x) = x^2 and g(x) = 2^x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is
Quantitative Aptitude – Algebra – Functions – Q3: If f(x) = (5x+2)/(3x-5) and g(x) = x^2 – 2x – 1, then the value of g(f(f(3))) is
Quantitative Aptitude – Algebra – Functions – Q4: If f1(x) = x^2 + 11x + n and f2(x) = x, then the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots, is
Quantitative Aptitude – Algebra – Functions – Q5: The area of the closed region bounded by the equation | x | + | y | = 2 in the two-dimensional plane is
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