Question

Let f(x)=1-(x-3)2, evaluate: (a) f(x+3), (b) f(3-x), and (c) f(2x+1). 

Answers:

(a) _____- ____2

(b) _____- _____2

(c) _____x2 +_______

Answer 1

(a) 1-(x+3-3)^2=1-x^2

(b) 1-(3-x-3)^2=1-(-x)^2=1-x^2 same as (a)

(c) 1-(2x+1-3)^2=1-(2x-2)^2=1-4(x-1)^2=1-4(x^2-2x+1)=1-4x^2+8x-4=-4x^2+8x-3

Answer 2

a.f(x+3)=1-((x+3)-3)2 since,f(x)=1-(x-3)2

f(x+3)=1-(x-0)2

ans :f(x+3)=1-2x

(b).f(3-x)=1-((3-x)-3)2 since ,f(x)=1-(x-3)2

f(3-x)=1-(0-x)2

ans: f(3-x)=1+2x

(c).f(2x+1)=1-((2x+1)-3)2

f(2x+1)=1-(2x-2)2

f(2x+1)=1-(4x-4)

f(2x+1)=1-4x+4

ans: f(2x+1)=5-4x

i like this question .it gives more thinking power