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Rational Functions
A rational function can have a variable like "x" in the numerator AND the denominator. When this happens, there are some special rules and properties to consider.
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\(f\) and \(g\) are functions defined as \(f(x) = 16 + \frac{9}{x}\) and \(g(x) = \frac{9}{x}\). What is the value of \((f+g)(18)\)?
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What is the nearest integer value of \[y=\frac{6x-23}{x-5}\] when \(x=10000\)?
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\(f\) and \(g\) are functions defined as \(f(x)= 5x + \frac{6}{2x-2}\) and \(g(x) = \frac{4x}{3x-2}\). What is the value of \(\left(f\circ g\right)(4)\)?
Note: \(f \circ g\) denotes the composition of the 2 functions.
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If the asymptotes of the graph \[y=\frac{7x+2}{x-2a}\] are \(x=24\) and \(y=b\), what is the value of \(ab\)?
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by Brilliant Staff