Find the domain and range of
f(x)=1/sin4x+cos4x
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Answer:
Step-by-step explanation:
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mounika1234:
it is not clearly visible
better not?
now
can u explain it clearly and visibly
when it comes to the domain, the denominator of the function has to be different from 0. so we look for those x who make the denominator zero and we take them away
when it comes to the Range the sine fonction can take any small values which means that the fonction can take any value BUT 0.
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Answer:
domain of f(x) = { x ∈ R / sin ( 4x - π/4 ) ≠ 0 }
range of f ( x ) = R\{0}
Step-by-step explanation:
1 / ( sin4x + cos4x ) = 1 / [√2 ( 1 /√₂ sin4x + 1 /√₂ cos4x ) ]
= 1 / [ √2 ( cos π/4 × sin4x + sin π/4 × cos4x ) ]
= 1 / [√2 × sin( 4x + π/4 ) ]
sin ( 4x + π/4 ) = 0
⇔ 4x + π/4 = kπ
⇔ 4x = kπ = π/4
⇔ x = ( kπ = π/4 ) /4 = [ ( 4k - 1 ) π ] / 16
domain of f(x) = { x ∈ R / sin ( 4x - π/4 ) ≠ 0 }
range of f ( x ) = R\{0}
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