document.write( "Question 1117852: Look at this function: 𝑓(𝑥) = ln(𝑥^2 + 2𝑥 − 2).
\n" ); document.write( "1.) What is the domain?
\n" ); document.write( "2.) What are the equations of all asymptotes of 𝑓(𝑥).
\n" ); document.write( "3.) Find the solution set (solve) for the inequality 𝑓(𝑥) ≤ 0, write the solution set in interval notation. \n" ); document.write( "

Algebra.Com's Answer #733052 by Boreal(15235) $\"\"$ $\"About$

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Look first at the graph of x^2+2x-2
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\n" ); document.write( "\n" ); document.write( "The roots are done using the quadratic formula
\n" ); document.write( "x=(1/2){-2+/- sqrt(4+8)}
\n" ); document.write( "This is -1+/-sqrt(3) or -1+sqrt(3) or x > 0.732.
\n" ); document.write( "This is -1-sqrt(3) or x < -1.732
\n" ); document.write( "When x is between those values, the ln does not exist
\n" ); document.write( "The domain is therefore (-oo, -2.732) and (0.732, oo)
\n" ); document.write( "From the left side, as x approaches -2.732 from the negative, or to 0.732 from the right, the ln becomes closer to 0 and the ln becomes large negative.
\n" ); document.write( "The asymptotes are x=-1-sqrt(3) and x= -1+sqrt (3)
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\n" ); document.write( "For the function being <0, one needs values of the quadratic less than 1, since ln (1) is 0, and greater than 0, since ln 0 doesn't exist.
\n" ); document.write( "x^2+2x-2=1
\n" ); document.write( "x^2+2x-3=0
\n" ); document.write( "(x+3)(x-1)=0
\n" ); document.write( "x=1, -3
\n" ); document.write( "So (-3, -1-sqrt(3)) and (-1+sqrt(3), 1) the function is < 0\r
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\n" ); document.write( "\n" ); document.write( " $\"graph%28300%2C300%2C-5%2C5%2C-10%2C10%2Cln%28x%5E2%2B2x-2%29%29\"$ \n" ); document.write( "

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