Question

f(1) = 1, f(2x) = 4f(x) + 5 and f (x + 2) = f(x) + 3x + 5 for all real values of x. Find the value of F (20).

Answer 1

Answer:

393

Step-by-step explanation:

f(20)=f(2x10)=4(f(10))+5

4[f(2x5)]+5

4[4.f(5)+5]+5

4(4x23+5)+5

4(92+5)+5

4(97)+5

388+5

393

f(2x1)= 4f(1)+5

f(2) = 4 + 5 = 9

f(1+2) = f(1)+ 3x1 +5

        = 1 + 3 + 5 = 9

f(4) = 4(9)+5

      = 36+5

      = 41

f(5) = f(3+2) = f(3)+ 3x3+5

                   =f(3)+ 14

                   = 9 + 14

                   =  23