Let the function f(x) be defined as f(x) = ₁₀ ₂ (6 - ₂(x^2 - 2x + 17)) + ⁻¹ ( x+1 2x-1 ) . The number of integers in the domain of f(x) is :

Step-by-step solution

For the first term to be defined, the argument of the outermost logarithm must be strictly positive: ₂ (6 - ₂(x^2 - 2x + 17)) > 0 6 - ₂(x^2 - 2x + 17) > 1 ₂(x^2 - 2x + 17) x^2 - 2x + 17 x^2 - 2x - 15 (x-5)(x+3) x (-3, 5) Note that x^2 - 2x + 17 = (x-1)^2 + 16 > 0 is always true, so the innermost logarithm is always defined. For the second term to be defined, the argument of the inverse cosine must lie in [-1, 1] : -1 x+1 2x-1 1 This is equivalent to | x+1 2x-1 | 1 Squaring both sides (since both sides are non-negat