is x^2 one to one?
155436
The function f(x)=x2 is not one-to-one because f(2) = f(-2). Its graph is a parabola, and many horizontal lines cut the parabola twice. The function f(x)=x 3, on the other hand, IS one-to-one. If two real numbers have the same cube, they are equal.
718003
Assuming the question is asking (√x)2 or √(x2) , which is then simplified to x , the answer is 1 .
1156785
Now if we have an irrational number x that cannot be written as the square root of a rational number, then x² is irrational. ... Now if we have an irrational number x that cannot be written as the square root of a rational number, then x² is irrational.
1044859
1! is simply one, because doing factorial means to reduce a number to 1 by multiplying all the numbers in between. And when you bring one to one itself , you do 1 ❌ 1 = 1. That's it! Note: This does not apply in case of zero factorial, it has got another way to prove.
1356246
Sooooo, “I” squared is the same thing as the square root of negative 1 times the square root of negative one. Since we know that square rooting and squaring are opposites, the two will cancel each other out, leaving you with negative 1.
574684
A function f is 1 -to- 1 if no two elements in the domain of f correspond to the same element in the range of f . In other words, each x in the domain has exactly one image in the range. ... If no horizontal line intersects the graph of the function f in more than one point, then the function is 1 -to- 1 .
1032156
A short proof of the irrationality of √2 can be obtained from the rational root theorem, that is, if p(x) is a monic polynomial with integer coefficients, then any rational root of p(x) is necessarily an integer. Applying this to the polynomial p(x) = x2 − 2, it follows that √2 is either an integer or irrational.
836121
{x | x ≥ 0}. If the domain of a function is all real numbers (i.e. there are no restrictions on x), you can simply state the domain as, 'all real numbers,' or use the symbol to represent all real numbers.
1193740
No. The square root of negative one, is not a rational number. The square of any rational number is always a positive number , but the square of is , which is not positive. ... It is a complex number, specifically a pure imaginary number.
214129
For example, x²+6x+9=(x+3)². However, even if an expression isn't a perfect square, we can turn it into one by adding a constant number. For example, x²+6x+5 isn't a perfect square, but if we add 4 we get (x+3)². This, in essence, is the method of *completing the square*.
760860
Secondly, one raised to any power is one. This, too, is logical, because one times one times one, as many times as you multiply it, is always equal to one. The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents.
762238
It is indeed true that "whenever both x and −x are in the domain of the square root function the function values agree" because (as you know quite well) only x=0 satisfies that hypothesis. So according to the strict reading of the definition, the square root function is even.
395011
A function f has an inverse function, f -1, if and only if f is one-to-one. A quick test for a one-to-one function is the horizontal line test. If a horizontal line intersects the graph of the function in more than one place, the functions is NOT one-to-one.
10344
In general, the square root of the square of a real number is always equal to the absolute value of that number. In other words, the equation sqrt(x2) = |x| is true for all real numbers x.
1075720
x multiplied by x is x^2, but x multipied with x means that the first with the second x multiplies a number [the with could be plus + or minus -].
833406
Yes, the difference of two polynomials is always a polynomial. ... To prove this, recall the definition of polynomials of one variable. They are finite sums of expressions of the form where a is a constant, x is the variable and k is a non-negative integer.
728451
Domain: So the domain of f(x) := tanx is all real numbers except x = π 2 + kπ, k an integer. All of the trig functions are periodic and thus are not one-to-one.