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A function f: R R is such that f( l )=2 and f(x+y)=f(x) f(y) x, y . The area (in square units) enclosed by the lines 2|x|+5|y| 4 expressed interms of f(1), f(2) and f(4) is

Options

  1. Af(4) f(1)+2 f(2)
  2. Bf(4) 1+f(2)
  3. C2 f(4) 2 f(1)+f(2)
  4. Df(4) 2 f(1)+f(2)

Correct answer

B. f(4) 1+f(2)

Step-by-step solution

Given, f(x+y)=f(x) f(y) f(x)=a^xf( 1 )=a^ l =2 a=2 f(x)=2^x Area enclosed by the lines 2|x|+5|y| 44 ( 1 2 2 4 5 )= 16 5 = 16 1+(2)^2 = (2)^4 1+(2)^2 = f(4) 1+f(2)

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