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Identify rational function from this equation
xf(x)−5f(x)−2=0xf(x)-5f(x)-2=0xf(x)−5f(x)−2=0
f(x)=2x−5f(x)=\frac{2}{x-5}f(x)=x−52
f(x)=1x2f(x)=\frac{1}{x^2}f(x)=x21
f(x)=1xf(x)=\frac{1}{x}f(x)=x1
Which of the following is a rational function?
f(x)=2x−1f(x)=2x-1f(x)=2x−1
f(x)=3x+1x2−4\ f(x)=\frac{3x+1}{x^2-4} f(x)=x2−43x+1
Complete:
The equation f(X)=P(x)Q(x),Q(X)≠0f(X)=\frac{P\left(x\right)}{Q\left(x\right)},Q(X)\ne0f(X)=Q(x)P(x),Q(X)=0 is the form of the ________ .
Rational function
Identity function
Empty function
f(x)=x2+12\ f(x)=\frac{x^2+1}{2} f(x)=2x2+1
f(x)=xf(x)=xf(x)=x
f(x)=2x−1x+1\ f(x)=\frac{2x-1}{x+1} f(x)=x+12x−1
f(x)=x2f(x)=x^2f(x)=x2
What is the general form of the rational functions?
f(x)=ax2+bx+cf(x)=ax^2+bx+cf(x)=ax2+bx+c
f(x)=g(x)h(x) where h(x)≠0\ f(x)=\frac{g\left(x\right)}{h\left(x\right)}\ where\ h(x)\ne0 f(x)=h(x)g(x) where h(x)=0
A rational function can be defined as:
A function with irrational roots
A function with a polynomial in the numerator and a polynomial in the denominator
A function with a trigonometric expression
yx−100=0yx-100=0yx−100=0
Y=10x2Y=\frac{10}{x^2}Y=x210
Y=100xY=\frac{100}{x}Y=x100
Y=1x2Y=\frac{1}{x^2}Y=x21
A function identified by the degrees of the numerator and denominator is called _________.
Real function
. Identify rational function from this equation
x2−2x+2=0.x^2-2x+2=0.x2−2x+2=0.
f(x)=2(x−5)f(x)=\frac{2}{\left(x-5\right)}f(x)=(x−5)2
f(x)=2x−2f\left(x\right)=\frac{2}{x-2}f(x)=x−22
f(x) = 2x−1x2+1f\left(x\right)\ =\ \frac{2x-1}{x^2+1}f(x) = x2+12x−1
It is done.