6.
f(x)=2x-1
g(x)=x²+4x
g(f(x))=?
g(2x-1)=(2x-1)²+4(2x-1)=4x²-4x+1+8x-4=
=4x²+4x-3
7.
18arccos²x-3π•arccosx-π²=0 x∈[-1;1]
arccosx=t
18t²-3πt-π²=0
D=(-3π)²-4•18•(-π²)=8π²+72π²=81π²
t=(3π-9π)/36= -π/6
t=(3π+9π)/36=π/3
arccosx=π/3=cosπ/3=1/2
arccosx= -π/6,т.к аrccos x∈[0;π] нет решения
х=1/2; х∈[-1;1]
ответ: х=1/2
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6.
f(x)=2x-1
g(x)=x²+4x
g(f(x))=?
g(2x-1)=(2x-1)²+4(2x-1)=4x²-4x+1+8x-4=
=4x²+4x-3
7.
18arccos²x-3π•arccosx-π²=0 x∈[-1;1]
arccosx=t
18t²-3πt-π²=0
D=(-3π)²-4•18•(-π²)=8π²+72π²=81π²
t=(3π-9π)/36= -π/6
t=(3π+9π)/36=π/3
arccosx=π/3=cosπ/3=1/2
arccosx= -π/6,т.к аrccos x∈[0;π] нет решения
х=1/2; х∈[-1;1]
ответ: х=1/2
1) Вычислить значение выражения: arcsin(1/√2)+ arccos(-1/2)+ arcctg√3.
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