CAT 2017 Question Paper | Quants Slot 1

CAT Questions

Functions as an idea is a fabulous idea if one can wrap their head around it the right way, and it has been one of the staple ideas tested by the CAT Exam historically. The question is about Function of a function. We need to find out the value of function of a function at x = 3. Function is a simple topic that involves a lot of basic ideas. Make sure that you get hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept of Functions questions in the CAT Exam.

Question 33 : If f(x) = \\frac{5x + 2}{3x - 5}) and g(x) = x² – 2x – 1, then the value of g(f(f(3))) is :

1. 2
2. \\frac{1}{3})
3. 6
4. \\frac{2}{3})

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Functions

Firstly, f(3) = \\frac{5(3) + 2}{3(3) - 5}) = \\frac{15 + 2}{9 - 5})
⟹ f(3) = \\frac{17}{4})
Now, let us find f(f(3))
f(f(3)) = \\frac{5(\frac{17}{4})) + 2}{3(\frac{17}{4})) - 5}) = \\frac{\frac{85 + 8}{4}}{\frac{51 - 20}{4}}) = \\frac{93}{31}) = 3.
Next, we can find g(f(f(3))).
g(f(f(3))) = x² - 2x - 1
g(f(f(3))) = (x - 1)² - 2
g(f(f(3))) = (3 - 1)² - 2 = 4 - 2 = 2

The question is "If f(x) = \\frac{5x + 2}{3x - 5}) and g(x) = x² – 2x – 1, then the value of g(f(f(3))) is :"

Hence, the answer is 2

Choice A is the correct answer