F and g are inverses by showing that f(g(x)) = x and g(f(x)) = x
Further explanation
f(x) = quantity x minus seven divided by quantity x plus two. It means we should write it as follows:
\(f(x) = \frac{x-7}{x+2}\)
And g(x) = quantity negative two x minus seven divided by quantity x minus one. It means we should write it as follows:
\(g(x)=\frac{-2x-7}{x-1}\)
F and g are inverses by showing that f(g(x)) = x and g(f(x)) = x
\(f(g(x)) = x \\f(g(x)) = \frac{\frac{-2x - 7}{(x-1) - 7} }{ \frac{-2x - 7}{(x-1) + 2} } \\f(g(x)) = \frac{ \frac{-2x - 7 - 7x + 7}{(x - 1)} }{ \frac{-2x - 7 + 2x - 2}{(x - 1)} } \\f(g(x)) = \frac{-9x}{-9} = x\)
\(g(x) = \frac{-2x - 7}{x - 1} \\g(x) = \frac{\frac{-2(x - 7)}{(x + 2) - 7}}{\frac{(x - 7)}{(x + 2) - 1} } \\g(x) = \frac{\frac{(-2x + 14 - 7x - 14)}{(x + 2)} }{\frac{(x - 7 - x - 2)}{x + 2} } \\g(x) = \frac{-9x}{-9} = x\)
Therefore:
It is confirmed that f and g are inverses by showing that \(f(g(x)) = g(f(x)) = x\).
Learn more
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Answer details
Grade: 5
Subject: Math
Chapter: inverses
Keywords: inverse, quantity, minus, divided, negative
