document.write( "Question 1199941: Find the inverse function of f(x)=-x^2+8x-14 and x ≤4. Find the domain of this inverse function. \n" ); document.write( "

Algebra.Com's Answer #834309 by Fombitz(32388) $\"\"$ $\"About$

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\n" ); document.write( " $\"y=-x%5E2%2B8x-14\"$
\n" ); document.write( "Now to find the inverse, interchange x and y and solve for y.
\n" ); document.write( "This new y is the inverse of the original function.
\n" ); document.write( " $\"x=-y%5E2%2B8x-14\"$
\n" ); document.write( " $\"y%5E2-8x%2B14=-x\"$
\n" ); document.write( "Complete the square,
\n" ); document.write( " $\"y%5E2-8x%2B16%2B14=-x%2B16\"$
\n" ); document.write( " $\"%28y-4%29%5E2%2B14=-x%2B16\"$
\n" ); document.write( " $\"%28y-4%29%5E2=2-x\"$
\n" ); document.write( " $\"y-4=+0+%2B-+sqrt%282-x%29\"$
\n" ); document.write( "The zero is the first term on the right hand side to make the plus/minus sign work correctly,
\n" ); document.write( " $\"y=4+%2B-+sqrt%282-x%29\"$
\n" ); document.write( "Since the term under the radical must be non-negative,
\n" ); document.write( " $\"2-x%3E=0\"$
\n" ); document.write( " $\"x%3C=2\"$ \n" ); document.write( "

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