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

January 1st, 2020 by

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

# Quantitative Aptitude – Algebra – Functions – Let f(x) = x^2 and g(x) = 2^x

January 1st, 2020 by

Quantitative Aptitude - Algebra - Functions - Let f(x) = x^2 and g(x) = 2^x Quantitative Aptitude - Algebra - Functions Question 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 A) 16 B) 18 C) 36 D) 40 Answer Option (C) Solution From CAT 2017 - Quantitative Aptitude - Algebra - Functions, we can see that, f(g(x)) = 2^(2x) g(f(x)) = 2^((x)^2) f(f(g(x)) + g(f(x)) = (2^(2x) + 2^(x^2))^2 at x = 1, we get 36 Option (C) Download CAT 2017 Question Paper with answers an

# Quantitative Aptitude – Algebra – Functions – If f(x) = (5x+2)/(3x-5)

December 30th, 2019 by

Quantitative Aptitude - Algebra - Functions - If f(x) = (5x+2)/(3x-5) Quantitative Aptitude - Algebra - Functions Question If f(x) = (5x+2)/(3x-5) and g(x) = x^2 - 2x - 1, then the value of g(f(f(3))) is A) 2 B) 1/3 C) 6 D) 2/3 Answer Option (A) Solution From CAT 2017 - Quantitative Aptitude - Algebra - Functions, we can see that, f(3) = 17/4 f(17/4) = 3 g(3) = 2 Option (A) Download CAT 2017 Question Paper with answers and detailed solutions in PDF CAT 2017 Questions from Quantitative Aptitude - Algebra - Fun

# Quantitative Aptitude – Algebra – Functions – If f1(x) = x^2 + 11x + n

December 30th, 2019 by

Quantitative Aptitude - Algebra - Functions - If f1(x) = x^2 + 11x + n Quantitative Aptitude - Algebra - Functions Question 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 Answer 24 Solution From CAT 2017 - Quantitative Aptitude - Algebra - Functions, we can see that, f1(x) = f2(x) x^2 + 11x +n = x x^2 + 10x + n =0 To have distinct and real roots, D>0 D = b^2-4ac = 100 – 4n > 0 On solving the inequality, we get, n

# Quantitative Aptitude – Algebra – Functions – The area of the closed region

December 30th, 2019 by

Quantitative Aptitude - Algebra - Functions - The area of the closed region Quantitative Aptitude - Algebra - Functions Question The area of the closed region bounded by the equation | x | + | y | = 2 in the two-dimensional plane is A) 4π B) 4 C) 8 D) 2π Answer Option (C) Solution As per the question from CAT 2017 - Quantitative Aptitude - Algebra - Functions, Remember the formula |x| + |y| = n Here, area bounded by the region = 2n^2 In the question, n=2 So, area = 8 Option (C) Download CAT 2017 Question Paper

# Quantitative Aptitude – Algebra – Functions – Let f(x)=max{5x, 52-2x^2}

December 22nd, 2019 by

Quantitative Aptitude – Algebra - Functions – Let f(x)=max{5x, 52-2x^2} Slot -2 – Quantitative Aptitude – Algebra - Functions – Let f(x)=max{5x, 52-2x^2}  Let f(x)=max{5x, 52-2x^2}, where x is any positive real number. Then the minimum possible value of f(x) is? Answer: 20 Solution: For f(x) to be minimum , 5 = 52 − 2^2 2^2+5 −52 =0 −42+13=0 = 4 Thus minimum value of f(x) = 5x = 5*4 = 20 Other posts related to Quantitative Aptitude – Modern Maths Permutation and Combination – Fundamental Principle

# Quantitative Aptitude – Algebra – Functions – If f(x + 2) = f(x) + f(x + 1)

December 21st, 2019 by

Quantitative Aptitude – Algebra - Functions – If f(x + 2) = f(x) + f(x + 1) Slot -1 – Quantitative Aptitude – Algebra - Functions – If f(x + 2) = f(x) + f(x + 1)  If f(x + 2) = f(x) + f(x + 1) for all positive integers x, and f(11) = 91, f(15) = 617, then f(10) equals? Answer: 54 Solution: Given , f(x + 2) = f(x) + f(x + 1) f(15) = f(13) + f(14) f(13) + f(14) = 617 ---------------1) f(12) + f(13) = f(14) -------------2) f(11) + f(12) = f(13)-------------3) from eq 1) , 2) & 3) 2f(11) + 3f(12) =