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2010-02-23T22:15:50+01:00
F(0), f(-1½), f(√₂), f(√₃+1), f(π), f(k)
a) f(x)=2√₃*x
f(0)=2√₃*0=0
f(-1½)=2√₃*(-1½)=-3√₃
f(√₂)=2√₃*√₂=2√₆
f(√₃+1)=2√₃*(√₃+1)=2*3+2√₃=6+2√₃
f(π)=2√₃π
f(k)=2√₃*k

b) f(x)=|x-√₂|
f(0)=|x-√₂|=|0-√₂|=|-√₂|=√₂
f(-1½)=|x-√₂|=|-1½-√₂|=1½+√₂
f(√₂)=|x-√₂|=√₂-√₂=0
f(√₃+1)=|x-√₂|=|√₃+1-√₂|=√₃+1-√₂
f(π)=|x-√₂|=|π-√₂|=π-√₂
f(k)=|x-√₂|=k-√₂

c) f(x)=(x+2)²-3
f(0)=(x+2)²-3=1
f(-1½)=(-1½+2)²-3=¼-3=-2¾
f(√₂)=(√₂+2)²-3=2+4√₂+4-3=4√₂+3
f(√₃+1)=(√₃+1+2)²-3=(√₃+3)²-3=3+6√₃+9=6√₃+12
f(π)=(π+2)²-3
f(k)=(k+2)²-3

d) f(x)=x/x-1
f(0)=0
f(-1½)= -1½ / -1½-1= 3/5
f(√₂)=√₂/√₂-1
f(√₃+1)=√₃+1 / √₃+1-1= √₃+1 / √₃ * √₃/ √₃ = 3+√₃ / 3
f(π)=π/π-1
f(k)=k/k-1