Verified answer

f(x+1) = x*f(x) e f(1/2) = √π

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x + 1 = 3/2

2x + 2 = 3

2x = 1

x = 1/2

f(1/2 + 1) = 1/2*f(1/2)

f(3/2) = 1/2*√π

f(3/2) = √π/2

f(x + 1) = x*f(x)

f(x) = k*x! (função fatorial)

f(1/2) = k*(1/2)! = k*√π/2 = √π --> k = 2

f(x) = 2*x!

f(3/2) = 2*(3/2)!

(3/2)! = 3√π/4

f(3/2) = 2*3√π/4 = 3√π/2

pronto