How do you find the inverse of an equation?
157110
It would be nice if you could just flip, but...\n\nYou need to change your y to x and your x to y.\n\nFor example:\n\ny=3log(x+6), would become\n\nx=3log(y+6), solve for y \n\nx/3 = log(y+6)\n\n10^(x/3) = y+6\n\ny = 10^(x+3)-6\n\nUse the same process for the others.
831674
1. replace x with -3, calculate and see if you get 0\n2. divide by (x+3) and solve the remaining quadratic equation
458222
0 1 0 0\n0 0 1 0\n1 0 0 0\n0 0 0 1\nPut the identity matrix behind your matrix.\nTurn you matrix into the identity matrix using row operations.  The matrix in the back will be the inverse.\n0 1 0 0  1 0 0 0 \n0 0 1 0  0 1 0 0 \n1 0 0 0  0 0 1 0 \n0 0 0 1  0 0 0 1\nSwap row 1 with row 3\n1 0 0 0  0 0 1 0 \n0 0 1 0  0 1 0 0 \n0 1 0 0  1 0 0 0 \n0 0 0 1  0 0 0 1\nSwap row 2 with row 3\n1 0 0 0  0 0 1 0 \n0 1 0 0  1 0 0 0\n0 0 1 0  0 1 0 0 \n0 0 0 1  0 0 0 1\nThus, the inverse is\n0 0 1 0\n1 0 0 0\n0 1 0 0 \n0 0 0 1
778162
Step 1: find y '\nStep 2: fill in x=1\nThat gives the right answer 2\n\nTh
797737
Ok, take your equation \nf(x) = 2x^2 - 10\n\nreplace f(x) with y\n\ny = 2x^2 - 10\n\nswap y and x\n\nx = 2y^2 - 10\n\nsolve for y\nto do this first add 10 to both sides\n\nx + 10 = 2y^2\n\ndivide both sides by 2\n\n(1/2)x + 5 = y^2\n\ntake the sqaure root of both sides\n\nsqrt((1/2)x + 5) = y\n\nchange y to f(x)^-1 [the inverse function notation]\n\nf(x)^-1 = sqrt((1/2)x + 5)\n\nhope this helps
323499
The inverse function is computed as below. In general, if you have a function of the form,\n\nf(x) = y, the inverse function is defined as \nx = f^(-1) (y), basically rearrange the equation so that you have the x on the left hand side of the equation.  This may not be always possible.\n\nIn the present case, when you solve for x,\ny = sqrt(x+5)\ny^2 = x + 5\nx = y^2 - 5\n\nhence the inverse function is y^2 - 5.
949784
y= (x^2 - 1)^2\nx^2-1=+/-√y\nx^2=1+/-√y\nx=+/-√(1+/-√y)
697874
Multiply or divide all components in one question to set the variables in the opposite questions to cancel out if you added the two problems together by combining like terms. For example:\n2x + 3y = -13  and 4x + y = -1\n\nTo keep this simple I will multiply all the components of the 2x + 3y = -13 equation by negative 2, resulting in:\n\n-4x - 6y = 26\n\nThen add the new equation to the other equation 4x + y = -1\n\n-4x -6y = 26\n4x + y = -1\n----------------\n0x -5y = 25  which simplifies to y = -5\n\nInsert the value found for y back into one of the original eqations and solve for x\n\n2x + 3(-5) = -13\n\n2x + -15 = -13\n\n2x = 2\n\nx = 1\n\nYour end result is x =1 and y = -5
874355
Using matices to do this\n\n[ 1 -2 1] * [x] = [-5]\n[ 2 -1 1]   [y]    [ 1]\n[2  1  2]   [z]    [10]\n\nAX = B\nA*A^(-1)X = A^(-1)B\nX = A^(-1)B\n\nSO we need the inverse of A this can be worked out using a long and tedious method or just use a calculator\n\nA^-1 = [ -.6 1 -.2]\n           [ -.4 0   2]   \n           [.8   -1 .6]\n\nA^-1B = [2}\n              [4}\n              [1]\nso x =2  y=4 z=1\n\n now you do the other one\nCheck\n2 - (4*2) +1 = 2 - 8 +1 = -5
752603
The inversion of a 3x3 matrix is very easy to solve, however the equation is fairly long. You can find it on wikipedia at http://en.wikipedia.org/wiki/Inverse_matrix#Inversion_of_3_x_3_matrices
1033116
A X = D\nX = A^(-1) D. (A inverse * D)\n Do it ur self.
984409
The goal here is to find the equation with x on one side and everything else on the other.  It's like the equation you have, but instead of y= you want x=.  So you need to "solve for x."  Think of y as just a number, and you need to find what x =.\n\nStep by step:\n\ny=4x+4\n\nSubtract 4 from each side:\n\ny-4=4x\n\nDivide both sides by 4\n\n(y-4)/4=x\n\nx=(y-4)/4\n\nThere's your equation!  Hope this helps.
459985
Find the inverse of the matrix\n5 -3\n4  2\nA 2x2 matrix has a formula for the inverse.\nThe inverse of the matrix\na b\nc d\nis \nd/(ad-bc) -b/(ad-bc)\n-c/(ad-bc) a/(ad-bc)\nThus, for the above problem\na = 5, b = -3, c = 4 and d = 2\nad-bc = 5(2) - (-3)(4) = 10+12 = 22\nThe inverse is\n1/11  3/22\n-2/11 5/22\nMultiply this times the  matrix\n-2\n5\n= \n(1/11)(-2) + (3/22)(5)\n(-2/11)(-2) + (5/22)(5)\n= \n1/2\n3/2\nThus, x = 1/2 and y = 3/2 or (1/2,3/2)\nFor the second one the matrix is\n3 2 2\n1 2 -1\n2 -4 1\nThe inverse of this is\n1/14 5/14 3/14\n3/28 1/28 -5/28 \n2/7 -4/7  -1/7\nTake the inverse times the matirix\n3\n5\n0\nto get the matrix\n2\n1/2\n-2\nAnswer: x = 2, y = 1/2 and z =-2 or (2,1/2,-2)
542416
5x^2-2x-3 = 0\n\nX= (-b(+or-) sqrt B^2-4ac)/2c\n\nX= -(-2)+ (sqrt4-4*5*-3)/-6 or,\n\nX= (-(-2) - (sqrt4-4*5*-3))/-6\n\nX=  (2+ 8)/-6,\n\nX= -5/3\n\nOr\n\nX = 2-8/(-6) = 1
437876
Take the derivative:\n\nf'(x) = 2x - 4\n\nSet the derivative equal to 0, and solve for x:\n\n0 = 2x - 4\nx = 2\n\nSub this value of x into the original equation to find the turning point:\n\nf(2) = (2)^2 - 4(2) + 1\nf(2) = -3\n\nSo, your turning point is (2, -3).\n\nAnd, since the x-squared term in the equation is positive, you know that this point is a minimum.\n\nDone and done.
916864
Ord(e^(4x)-1 -4x) ~ Ord(e^(4x) > Ord(x^2)\nThen:\n\nlim(e^(4x)-1 -4x)/x^2 {x--> oo} = oo\n\nRemember\n\nln x < x^a < e^x < x^x
813596
Okay, the goal here is to get values of x that fit the equation.  These are not like easy linear ones, they have x^2 in them.  We can still solve them.  \n\nx^2=16\nWhat is the reverse sign of the square?  It's the square root.  Square root both sides and get\nx=sq(16)\nSo x=+/-4\nBoth work because (-4)^2 becomes 16 as well.  Those are your answers.\n\n\n2x(x+3)=0\nThe goal here is to make this equation equal zero.  Do you see how there are two "factors?"  Things that are multiplied together?  Well, to equal zero, one of them must equal zero.  Either one can equal zero, so you have different solutions that work.\n\nTake 2x:\n2x=0\nx=0\n\nNow x+3:\nx+3=0\nx=-3\nSo\nx=0,-3\n\n\nHere we have to "factor" this equation:  Find two things that, when multiplied together, equal this.  y^2 and 8y both have y, so factor out the y and get:\ny(y+8) \nWe can do as we did before, and get\ny=0\nand \ny+8=0, so\ny=-8\nOur answers are\ny=0,-8\n\nThe next two are harder:\n\nFirst bring the 28 over to the other side:\n\nx^2+3x-28=0  \n\nThe factored form of this actually has two factors, but none with just x.  To factor this, we need two factors of -28.  When one of them is multiplied by x and added to the other one multiplied by x, they equal 3x.  Now, a negative times a positive is a negative so we are looking for one positive and one negative factor of 28.  Let's try these two:\n\n7 and -4.\n7(-4)=-28\n7x+(-4x) = 7x-4x=3x!\n\n-4 and 7 are our factors, so:\n(x+7)(x-4) is our factored form.  Solve the components:\nx+7=0\nx=-7\n\nx-4=0\nx=4\n\n x=-7,4 are our two answers.\n\n\n\n2x^2+9x-5\n\n\nThe next one is similar, but more complicated.  We have a 2x^2.  No matter.  We need to find two factors of -5, and one of them will be multiplied by 2x instead of x.  The only factors of -5 are +/-1, and +/-5.  It looks like the 5 will be positive since 9x is fairly big and positive.  Let's try -1 and 5:\n2x(5)=10x\nx(-1)=-x\n10x+(-x)= 10x-x=9x!\n\nSo 2x will be multiplied by 5, and x by -1.  In factored form, this is:\n\n (2x-1)(x+5)\n\nBecause you use FOIL (first outside, inside last) so the 2x is not multiplied by -1, but by 5.  Now solve these components.\n\n2x-1=0\n2x=1\nx=1/2\n\nx+5=0\nx=-5\nSo\n x=1/2, -5 are our two answers. \n\nAll done.  Hope this helps.