document.write( "Question 64824: FOR THE FUNCTION DEFINED BY $\"f%28x%29=2-x%5E2\"$ , $\"0%3Cx\"$ , USE A SKETCH TO HELP FIND A FORMULA FOR f^-1(x). \n" ); document.write( "

Algebra.Com's Answer #45334 by funmath(2933) $\"\"$ $\"About$

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FOR THE FUNCTION DEFINED BY $\"f%28x%29=2-x%5E2\"$ , $\"0%3Cx\"$ , USE A SKETCH TO HELP FIND A FORMULA FOR f^-1(x).
\n" ); document.write( " $\"f%28x%29=2-x%5E2\"$ Is graphed below. Ignore the left side of the graph because the domain includes only positive values. I have also graphed the line y=x, because inverse functions are reflected about that line.
\n" ); document.write( " $\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C2-x%5E2%2Cx%29\"$
\n" ); document.write( "Notice that the graph has a y-intercept of (0,2), therefore the inverse will have an x-intercept of (2,0). Notice also that the graph goes toward -infinity as x goes towards +infinity, therefore its inverse will have x's that go to -infinity as y goes to positive infinity.
\n" ); document.write( "The parent f(x)=x^2, therefore the parent f^-1(x)=sqrt(x), it has a horizontal reflection so f^-1(x)=sqrt(-x). It also has a horizontal shift right 2 units, so the inverse function is:
\n" ); document.write( "f^-1(x)= $\"sqrt%282-x%29\"$
\n" ); document.write( "The graph of the inverse is below:
\n" ); document.write( " $\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2Csqrt%282-x%29%29\"$
\n" ); document.write( "If you aren't being taught about reflections and shifts, plot the points for f(x) and then reverse the x's and y's and you'll have the inverse.
\n" ); document.write( "Happy Calculating!!!
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