Question

domain of f(x) = √log_2 (5x-x^2/4 )
5х - x^2/4 >0
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Answer 1

f (x) = √log10 [5x – x2] / 4

= [log10 [5x – x2] / 4]½

[log10 [5x – x2] / 4] ≥ 0

[5x – x2] / 4 ≥ 1

[5x – x2] ≥ 4

x2 – 5x + 4 ≤ 0

(x – 4) (x – 1) ≤ 0

x ∈ [1, 4] and

[5x – x2] / 4 > 0

[5x – x2] > 0

x2 – 5x < 0

x (x – 5) < 0

x ∈ [0, 5]

x ∈ [1, 4]