f(2x-1)＝x^2+x

let

y=2x-1

x= (1/2)(y+1)

f(2x-1)＝x^2+x

f(y)=[(1/2)(y+1)]^2 + [(1/2)(y+1)]

=(1/4)(y+1)^2 + (1/2)(y+1)

=(1/4)y^2 + y + 3/4

ie

f(x) =(1/4)x^2 + x + 3/4