题目

1.given the function f(x) = x*2 -4x -5,find the values of:
a) f(k-2) b) f(x*2) - x*2 f(1)
2.given two functions f(x) = x*2 -3 and g(x) = 3x-4,find the values of:
a) f(k+1) -g(k-1) b) f(g(x)) c) g(f(x))
3.let f(x) = 1/1-x,find
a) f(f(x)) b) f(f(f(x))) c) f( 1/f(x) ) d) f (1/f(f(x)) )
感激不尽!

提问时间：2020-10-11

答案

1.a) f(k-2)=(k-2)²-4(k-2)-5=k²-8k-9
b) f(x²)-x²f(1)=(x²)²-4x²-5-x²(1²-4-5)=x^4-4x²-5+8x²=x^4+4x²-5
2.a) f(k+1)-g(k-1)=[(k+1)²-3]-[3(k-1)-4]=k²+2k-2-3k+7=k²-k+5
b) f(g(x))=(3x-4)²-3=9x²-24x+13
c) g(f(x))=3(x²-3)-4=3x²-13
3.a) f(f(x))=1/[1-(1/(1-x))]=(1-x)/(1-x-1)=(x-1)/x
b) f(f(f(x)))=1/[1-((x-1)/x)]=x/[x-(x-1)]=x
c) f(1/f(x))=f(1-x)=1/[1-(1-x)]=1/x
d) f(1/f(f(x)))=f(x/(x-1))=1/[1-x/(x-1)]=(x-1)/(x-1-x)=1-x