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antonner
@antonner
August 2022
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Решить функции 1.1-1.4
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MAXIS95
1.1 f(0)=2
f(1)=0
f(2)=0
f(3)=2
f(-x)=x²+3x+2
f(1/x)=1/x²-3/x+2
f(x+1)=x²+2x+1-3x-3+2=x²-x+3
1.2 ф(пси(х))=2^(2x)
пси(ф(х))=2^(x^2)
1.3 f(f(x))=1/(1-1/(1-x))=-(1-x)/x
f(f(f(x)))=1/(1-1/(1-1/(1-x)))=1+x/(1-x)
1.4 a)y=2x+3
2x=y-3
x=(y-3)/2
y=(x-3)/2
б)y=∛(1-x³)
y³=1-x³
x³=1-y³
x=∛(1-y³)
y=∛(1-x³)
в)y=sin(x/2)
x/2=arcsiny
x=2arcsiny
y=2arcsinx
2 votes
Thanks 1
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Answers & Comments
f(1)=0
f(2)=0
f(3)=2
f(-x)=x²+3x+2
f(1/x)=1/x²-3/x+2
f(x+1)=x²+2x+1-3x-3+2=x²-x+3
1.2 ф(пси(х))=2^(2x)
пси(ф(х))=2^(x^2)
1.3 f(f(x))=1/(1-1/(1-x))=-(1-x)/x
f(f(f(x)))=1/(1-1/(1-1/(1-x)))=1+x/(1-x)
1.4 a)y=2x+3
2x=y-3
x=(y-3)/2
y=(x-3)/2
б)y=∛(1-x³)
y³=1-x³
x³=1-y³
x=∛(1-y³)
y=∛(1-x³)
в)y=sin(x/2)
x/2=arcsiny
x=2arcsiny
y=2arcsinx