CAT 2020 Quant Question [Slot 3] with Solution 08

Question

If \(f(x + y) = f(x)f(y)\) and \(f(5) = 4,\) then \(f(10) - f( - 10)\) is equal to

  1. 0
  2. 15.9375
  3. 3
  4. 14.0625
Option: 2
Solution:

Given \(f(x + y) = f(x)f(y)\)

\( \Rightarrow f(x) = {a^x}\)( where \(a\) is a constant ) Given, \(f(5) = 4 \Rightarrow {a^5} = 4 \Rightarrow a = {2^{2/5}}\)

\(f(10) - f( - 10) = {a^{10}} - {a^{ - 10}} = {\left( {{2^{\frac{2}{5}}}} \right)^{10}} - {\left( {{2^{\frac{2}{5}}}} \right)^{ - 10}}\)

\( = {2^4} - {2^{ - 4}} = 16 - \frac{1}{{16}} = 15.9375\)

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