If fx- -log1-2 x2 - 2x - 2 - then domain of fx is

The correct option is A R log_ 1/2 #160; ( x ^ 2 2x+2)≥ 0 x ^ 2 2x+2≥ 1 and x^2 2x+2 gt;0 x ^ 2 2x+1≥ 0 (x 1) ^ 2 ≥ 0 x∈ R ...

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Definition of Functions

If fx= √log1...

Question

If f(x)= $\sqrt{{log}_{\frac{1}{2}} (x^{2} - 2 x + 2)}$ , then domain of $f (x)$ is

R

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R - {1, 2}

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R^{+}

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R - (1, 2)

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Solution

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f (x) = \sqrt{{log}_{1 / 2} (x^{2} - 2 x + 2)}

f (x) = \{\begin{matrix} \frac{x^{4} - 5 x^{2} + 4}{|(x - 1) (x - 2)|}, & x \neq 1, 2 \\ 6, & x = 1 \\ 12, & x = 2 \end{matrix}

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f (x) = x^{2} - 2 x

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f (x) = \frac{sin (log (x^{2} - 4 x + 4))}{([x] - 1)}

[.]

2^{x} + 2^{f (x)} = 2

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