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Which of the following is a rational function?
f(x)=2−xx−1\ f(x)=\frac{2-x}{x-1} f(x)=x−12−x
f(x)=3x2f(x)=3x^2f(x)=3x2
f(x)=x2+12\ f(x)=\frac{x^2+1}{2} f(x)=2x2+1
f(x)=xf(x)=xf(x)=x
f(x)=2x2−4f(x)=2x^2-4f(x)=2x2−4
f(x)=x2x−4\ f(x)=\frac{x^2}{x-4} f(x)=x−4x2
Complete:
A function identified by the degrees of the numerator and denominator is called _________.
Rational function
Identity function
Real function
Identify rational function from this equation
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
f(x)(x2−1)−2x=0f(x)(x^2-1)-2x=0f(x)(x2−1)−2x=0
f(x)=2x(x2−1)f\left(x\right)=\frac{2x}{\left(x^2-1\right)}f(x)=(x2−1)2x
f(x)=2(x2−1)f\left(x\right)=\frac{2}{\left(x^2-1\right)}f(x)=(x2−1)2
f(x)=x(x2−1)f\left(x\right)=\frac{x}{\left(x^2-1\right)}f(x)=(x2−1)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
f(x)=x2+5f(x)=x^2+5f(x)=x2+5
f(x)=x−32\ f(x)=\frac{x-3}{2} f(x)=2x−3
Write ratioanl function of this equation
(4x+1)−(3x−1)\left(\frac{4}{x+1}\right)-\left(\frac{3}{x-1}\right)(x+14)−(x−13)
−2〖x2−1)\frac{-2}{〖x^2-1)}〖x2−1)−2
−1〖x2−1)\frac{-1}{〖x^2-1)}〖x2−1)−1
−2〖x2+1)\frac{-2}{〖x^2+1)}〖x2+1)−2
These are functions in the formf(x)=g(x)h(x) where h(x)≠0.f\left(x\right)=\frac{g\left(x\right)}{h\left(x\right)}\ where\ h\left(x\right)\ne0.f(x)=h(x)g(x) where h(x)=0.
Linear functions
Rational functions
It is done.