Question

find the domain of the real function f(x)=x2-1/x2+1 step by step explanation pls...​

Answer 1

Answer:

For this type of function, the domain is all real numbers. A function with a fraction with a variable in the denominator. To find the domain of this type of function, set the bottom equal to zero and exclude the x value you find when you solve the equation.

Explanation:

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Answer 2

Answer:

You can compute the expression for any (real) value of x .

For the codomain, try and solve the equation

y=x21+x2

This becomes y+x2y=x2 , so

x2=y1−y

Since x2≥0 and every nonnegative number has a square root, the solution will be found if and only if

y1−y≥0

which amounts to 0≤y<1 . So the range is the interval [0,1) .

With calculus it’s easier: we see that, with f(x)=x2/(1+x2) ,

limx→−∞f(x)=limx→∞f(x)=1

and also

f′(x)=2x(1+x2)2

so that f is strictly decreasing over (−∞,0] and strictly increasing over [0,∞) . Since f(0)=0 , this and the limits above tell us that the range is [0,1) .