Question

1 point
If L{F(t)} = F (s), then L{F(at)} =
199
1
F ()
Option 1
0 Option 3
(-3)
11)
Option 2
O Option 4
​

Answer 1

Answer:

f(x + y) = f( x ). f( y )

if we put x = y = 1

f( 1 + 1) = f( 1 ) .f( 1 )

f(2) = 3 . 3

f(2) = 9

putting , x = 2 and y = 1

f( 2 + 1) = f(2).f(1)

f(3) = 9 × 3

f(3) = 27

putting , x = 3 , y = 1

f(3 + 1) = f(3).f(1)

f(4) = f(3) .f(1)

f(4) = 27 × 3

f(4) = 81

∑^{n}_{x=1} f(x) = 120

f(1) + f(2) + f(3) + + f(n) = 120

3 + 9 + 27 + + n terms = 120

we see series is in GP

first term ( a) = 3

common ratio ( r) = 3

then, Sn = a( rⁿ - 1)/(r - 1)

3(3ⁿ - 1)/(3 - 1) = 120

(3ⁿ - 1) = 40 × 2

3ⁿ - 1 = 80

3ⁿ = 81

3ⁿ = 3⁴

n = 4