Find the range of f(x)=2 sin^(8)x-3 sin^(4)x+2
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Answered by
35
Answer:
Range = 7/8 to 2
Step-by-step explanation:
Find the range of f(x)=2 sin^(8)x-3 sin^(4)x+2
f(x) = 2Sin⁸x - 3Sin⁴x +2
= 2Sin⁸x - 3Sin⁴x + 9/8 - 9/8 + 2
= 2Sin⁸x - (3/2)Sin⁴x - (3/2)Sin⁴x + 9/8 + 7/8
= Sin⁴x(2Sin⁴x - 3/2) - (3/4)(Sin⁴x - 3/2) + 7/8
= (2Sin⁴x - 3/2)( Sin⁴x - 3/4) + 7/8
= 2( Sin⁴x - 3/4)( Sin⁴x - 3/4) + 7/8
= 2( Sin⁴x - 3/4)² + 7/8
( Sin⁴x - 3/4)² min value = 0
f(x) = 7/8 min
Sin⁴x lies betwen 0 & 1
( Sin⁴x - 3/4)² max when x = 0
=> 9/16
f(x) = 2*9/16 + 7/8 (max)
Range = 7/8 to 2
f(x) = 2
Answered by
4
Answer:
range of this function is [7/8,2]
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