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What is the domain and range of # f(x) = x / (3x(x-1))#? - Socratic
Domain f(x): {x epsilon RR | x != 0, 1} In order to determine the domain, we need to see which part of the function restricts the domain. In a fraction, it is the denominator. In a square root function, it is what's inside the square root. Hence, in our case, it is 3x(x-1). In a fraction, the denominator can never be equal to 0 (which is why the denominator is the restricting part of the ...
How do you find the absolute value of the complex number
Take the square root of the sum of the real part squared plus the imaginary part squared. For real numbers, we find the distance of the number from 0 on the x-axis. In this case, we have a complex number with a real part and an imaginary part. On a coordinate plane, we would use the y-axis as the imaginary axis 'i' and plot this complex number at (-4, 1). Next, find the distance of that point ...
How do you solve the inequality 9x^2-6x+1<=0? - Socratic
9x^2-6x+1=9(x-1/3)^2<=0 when x=1/3. Actually the left side can never be less than 0 for real numbers. It's lowest value is f(x)=0 for x=1/3 You can see that from a diagram: Since this is precalculus, I'm in doubt if derivation should be used in the solution, but using it you can show that a tangent at x=1/3 has the inclination 0, i.e. is horisontal. Therefore the lowest point of the left side ...
What is the value of a^2+b^2? - Socratic
Let a and b be real numbers such that (a^2+1)(b^2+4) = 10ab - 5. What is the value of a^2+b^2? Algebra. 2 ...
How do you find the domain and range of y=-x^2-3x-3? - Socratic
Domain: x in RR Range: {y|y<=-3/4} The function is defined for all real x, so the domain is just the real numbers, RR. To find the range, we will consider the function as a parabola. Since the x^2 term is negative, we know the parabola will be concave down (nn). Therefor the range will be between -oo and the vertex of the parabola. The x coordinate of the vertex of a parabola ax^2+bx+c can be ...
How do you find the domain and range and determine whether ... - Socratic
The relation is a function. The domain and range are both all real numbers, or (-oo, oo) First, this relation is a function. A function means that the input only has ONE output, or that each x-value can only have ONE y-value. This equation y = 7x - 6 is a line on the graph. All non-vertical lines are functions. Also, since it is a line, that means that the domain and range are both all real ...
How do you solve abs(x^2 - 2x - 16) = 8? - Socratic
Recall the definition of the absolute value: |C|=C for all C>=0 and |C|=-C for all C<0. Let's divide the real numbers into two separate areas: A1 is a set of all real numbers x, for which x^2-2x-16 >= 0. A2 is a set of all real numbers x, for which x^2-2x-16 < 0. Let's determine these areas. Graphically, x^2-2x-16 is represented by a parabola with its two "horns" directed upwards. Therefore ...
If f(x) = 3x-6 and g(x) = x-2, what is f/g and its domain? - Socratic
The domain of this function is all Real numbers where #(x - 2) != 0# or where #x != 2# Answer link.
Can someone prove to me that multiplication by imaginary numbers is a ...
The Real numbers are usually thought of as constituting a line which we call the Real line. This is the #x#-axis of the Complex plane, representing an extension of the Real numbers to numbers of the form #a+bi#, where #i# is the imaginary unit (i.e. the point #(0, 1)#). Addition of complex numbers is two dimensional vector addition, that is:
What is the opposite and reciprocal of 7? + Example - Socratic
If you picture the real numbers on a line with #0# in the centre, the opposite of a number is on the opposite side of #0# at the same distance. The reciprocal is the multiplicative inverse. #7 * (1/7) = 1# where #1# is the identity for multiplication. When you are dealing with fractions, just swap the top and bottom to form the reciprocal.
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