Question

求下列函数解析式.已知f(x)=2x+3,g(2x-1)=f(x^2-1),求g(x)

Answer 1

g(2x-1)=f(x²-1)=2(x²-1)+3=2x²+1

令2x-1=t 则x=(t+1)/2

g(t)=2[(t+1)/2]²+1=(t+1)²/2+1

=(1/2)t²+t+3/2

所以g(x)=(1/2)x²+x+3/2