Problem simplifying composite functions!
- Thread starter VinZie
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Are you aware that the simplification does not care where the expression came from? Given an algebraic expression of some complexity, just simplify it. It matters not how it was created.
f(x) = x / (x-5) for x <> 5.
g(x) = 4/x for x <> 0.
f(g(x)) = f(4/x) = (4/x)/((4/x) - 5)
g(f(x)) = g(x / (x-5)) = 4/(x / (x-5))
What's stopping you from simplifying those?
f(x) = x / (x-5) for x <> 5.
g(x) = 4/x for x <> 0.
f(g(x)) = f(4/x) = (4/x)/((4/x) - 5)
g(f(x)) = g(x / (x-5)) = 4/(x / (x-5))
What's stopping you from simplifying those?
Dr.Peterson
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What you are really asking for is, how to simplify complex fractions.
One way that works well especially for your f(g(x)) is to multiply the entire numerator and the entire denominator by the LCD of the "little" fractions, namely x in that case.
For g(f(x)), you might prefer just restating the division by a fraction as multiplication by its reciprocal.
HallsofIvy
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Once you have \(\displaystyle \frac{\frac{4}{x}}{\frac{4}{x}- 5}\), multiply both numerator and denominator by x to get \(\displaystyle \frac{4}{4- 5x}\).
These aren't technical suggestions but
When you mean f(x) do not write (x); sooner or later, you will treat (x) as x instead of f(x) and make some absurd error. It is better to abbreviate f(x) as f.
Don't squeeze your writing into the smallest possible space. Paper is cheap. If you can barely see what you have written, you will make unnecessary errors. I see it all the time with students I tutor face to face.
When you mean f(x) do not write (x); sooner or later, you will treat (x) as x instead of f(x) and make some absurd error. It is better to abbreviate f(x) as f.
Don't squeeze your writing into the smallest possible space. Paper is cheap. If you can barely see what you have written, you will make unnecessary errors. I see it all the time with students I tutor face to face.