document.write( "Question 298792: Are functions f(x) = -1/4x + 5/4 and g(x) = -4x + (2.5/.5) inverses of each other? Why? \r
\n" ); document.write( "\n" ); document.write( "Must be solve in algebraic based. \n" ); document.write( "

Algebra.Com's Answer #214876 by nyc_function(2741) $\"\"$ $\"About$

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We can use the Round-Trip Theorem to show that if both functions = x, then they are inverses of each other.\r
\n" ); document.write( "\n" ); document.write( "In other words, if g(f(x)) = x and f(g(x)) = x, then the functions are inverses of each other.\r
\n" ); document.write( "\n" ); document.write( "g(f(x)) = -4[(-x/4) + 5/4] + 2.5/0.5\r
\n" ); document.write( "\n" ); document.write( "g(f(x)) = (x - 5) + 2.5/0.5\r
\n" ); document.write( "\n" ); document.write( "g(f(x)) = x - 5 + 5\r
\n" ); document.write( "\n" ); document.write( "g(f(x)) = x\r
\n" ); document.write( "\n" ); document.write( "Now, I will plug the value of g(x) into f(x). If I get x as the answer, then both functions are inverses of each other.\r
\n" ); document.write( "\n" ); document.write( "f(g(x)) = (-1/4)[(-4x) + (2.5/0.5)] + (5/4)\r
\n" ); document.write( "\n" ); document.write( "f(g(x)) = (x - (5/4) + (5/4)\r
\n" ); document.write( "\n" ); document.write( "f(g(x)) = x \r
\n" ); document.write( "\n" ); document.write( "As you can see they both = x and so they are both inverses of each other.\r
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