Find the inverse of f(x)=7x-2.?
604301
We just interchange the x's and the y's. then find what is y\nExample the inverse of f(x)=x+1\nSince f(x) is just equivalent to y... \nthen y=x+1. we then switch...\nx=y+1... then find for y... y=x-1. \nThat is the inverse of f(x)=x+1\nNow let's solve your problem\ny=f(x)=7x-2\ny=7x-2\nswitch x and y \nx=7y-2\nsolve for y\n(x+2)/7=y\ninverse is (x+2)/7
988496
(2x)/7 = (x-1)/3  Multiply both sides by 21\n\n6x = 7x –7 (-7x from both sides)\n\n-x = -7\n\nx = 7
958467
Replace x with 2:\nf(2)=2^3-4(2)^2+14(2)-20\nf(2)=8-16+28-20\nf(2)=-8+8\nf(2)=0
854860
(3x - a)(x - 2)(x - 7) = \n(3x - a)(x^2 - 7x - 2x + 14) = \n(3x - a)(x^2 - 9x + 14) = \n3x^3 - 27x^2 + 42x - ax^2 + 18ax - 14a\n3x^3 + (-27 - a)x^2 + (42 + 18a)x - 14a\n\n3x^3 - 32x^2 + 81\n\nso\n\n(-27 - a)x^2 + (42 + 18a)x - 14a = -32x^2 + 81\n(-27 + 32 - a)x^2 + (42 + 18a)x + (-14a - 81) = 0\n(5 - a)x^2 + (42 + 18a)x - (14a + 81) = 0\n(-a + 5)x^2 + (18a + 42)x - (14a + 81) = 0\n-(a - 5)x^2 + (18a + 42)x - (14a + 81) = 0\n\nx = (-b ± sqrt(b^2 - 4ac))/(2a)\n\nx = (-(18a + 42) ± sqrt((18a + 42)^2 - 4(-(a - 5)(-(14a + 81)))/(2(-(a - 5))\n\nx = (-(18a + 42) ± sqrt(((18a + 42)(18a + 42)) - 4(a - 5)(14a + 81)))/(-2(a - 5))\n\nx = (-(18a + 42) ± sqrt((324a^2 + 756a + 756a + 1764) - 4(14a^2 + 81a - 70a - 405))) / (-2(a - 5))\n\nx = (-(18a + 42) ± sqrt(324a^2 + 1512a + 1764 - 4(14a^2 + 9a - 405))) / (-2(a - 5))\n\nx = (-(18a + 42) ± sqrt(324a^2 + 1512a + 1764 - 56a^2 - 36a + 1620))) / (-2(a - 5))\n\nx = (-(18a + 42) ± sqrt(268a^2 + 1476a + 3384)) / (-2(a - 5))\n\nx = (-6(3a + 14) ± sqrt(4(67a^2 + 369a + 846)))/(-2(a - 5))\n\nx = (-6(3a + 14) ± 2sqrt(67a^2 + 369a + 846)) / (-2(a - 5))\n\nx = (3(3a + 14) ± sqrt(67a^2 + 369a + 846))/(a - 5)\n\nUnless you mistyped something, 3x^3 - 32x^2 + 81 does not factor into (3x - a)(x - 2)(x - 7)\n\n--------------------------------------------------------------------------------\n\nx^3 - x^2 + 16x - 16\n(x^3 - x^2) + (16x - 16)\nx^2(x - 1) + 16(x - 1)\n(x^2 + 16)(x - 1)\n\nif you were to take this further, then\n\n(x - 4i)(x + 4i)(x - 1)
1149949
multiply both sides by the reciprocal of the coefficient of x:\n\n(-7/4)(-4/7)x=(-7/4)(2/5)\n\nx=(-7/10)
932643
4x + 7 = -7\n4x = 14\nx = 14/4\nx = 7/2
830360
9x-(-2x) = 5x+4x-{2(x-10+3+7)}(-1) = 5x +2x-11x+22x-5x-x+x(-1)\n\n= 11x
1041171
f'(x) = 11ln(5x^2+7x) + 11x(10x+7)/(5x^2+7x) using the product rule.\n\nf'(2) = 11ln(5*2^2+7*2) + 11(2)(10*2+7)/(5*2^2+7*2)\n= 11ln(34) + 594/34\n= 56.260554006071892933393257662056
461122
Since f(x) is a polynomial of degree two in x,\nLet f(x) = ax^2 + bx + c, where a,b,c are constants.\n\nLet's find f(x) first.\n\nf(0) = 1 implies, c = 1.\n\nf(1) = 3 implies, a + b + c = 3\nor  a + b = 2 , or b = 2 - a  ...(1)\n\nf(-1) = 5 implies, a - b + c = 5\nor a - b = 4 ...(2)\n\nSubstituiting (1) into (2), we get,\n\na - [ 2 - a  ] = 4\n2a = 6 or a = 3.\nThus, b = 2 - a = 2 - 3 = -1.\n\nHence, f(x) = 3x^2 - x + 1\n\nNote that by long division or by the identity below,\n\n3x^2 - x + 1 = 3(x + 1)^2 - 7x - 2\n             \nWe get,\n\n[ 3x^2 - x + 1 ] /[1 + x]^2 = 3 - [7x + 2]/ [1 + x]^2   \n\nAnd that together with below,\n\n[7x + 2]/ [1 + x]^2  = 7 /(x + 1) - 5 /(x+1)^2\n\nGives,\n\n[ 3x^2 - x + 1 ] /[1 + x]^2 = 3 - 7 /(x + 1) + 5 /(x+1)^2\n  \nNow, we have an "integratable form".\n\n∫ [f(x) / (1 + x)^2] dx\n\n= ∫ [3x^2 - x + 1] / (1 + x)^2] dx\n\n= ∫ [ 3 - 7 /(x + 1) + 5 /(x+1)^2 ] dx\n \n= 3x - 7 log(x + 1) - (5/[x + 1]) + C\n\nwhere C is any arbitary constant.\n\nNote: Sometimes log(x + 1) can also be written as ln (x + 1)\n\nRemark. It is generally accepted that log and ln are both in base "e", the Euler number. If its in a different base, then usually its said or stated. For example logarithm of x in base 2 can be written as log_2(x).\nJust symbols :)\n\nRegards
201836
inverse of 1/2 = 2/1 = 2\n\nunless you have X^(1/2) = sqrt(X)
373083
Well, I'm not going to answer the question for you, but I'll tell you how to do it.\n\nWhen you're graphing the function, you set up a table with f(x) and x as the two columns, then solve for x for any set of numbers, like -3, -2, -1, 0, 1, 2, 3, and that's probably more than enough. Graph those on a piece of graph paper (f(x)=y, and then x). \n\nNow, to find the INVERSE, you simple switch the X and the Y. Instead of solving for x, you solve for f(x). So, your problem would be written x= -2/3y + 5. An easier way to do it, take the table you made before, and switch the columns, so that the solutions for x are underneath f(x) and the numbers you picked for f(x) are underneath the x column. Graph those coordinates. When you look at the graph, the inverse should be a mirror reflection of the first one, with  the graph of y=x as the line of symmetry. \n\nThat's how you find the inverse of any problem. Sorry if anything's unclear, if you need a better visual, I'm sure you could google up this exact method.
822098
2x - 7 = -4x - 1\n\nFirst, add 4x to both sides\n\n2x + 4x -7 = -1\n\nAdd like terms\n\n6x -7 = -1\n\nAdd 7 to both sides\n\n6x = 6\n\nDivide both sides by 6\n\nx = 1
889431
1. Find the antiderivative of 2x + 2sin(x).\nIt is f'(x) = x^2 - 2cos(x) + C\nSince f'(0) = 2, then you can plug in 0 for x and set this equal to 2.\n0^2 - 2cos(0) + C = 2\n-2 + C = 2\nC = 4\nf'(x) = x^2 - 2cosx + 4\nNow find this antiderivative.\nf(x) = (1/3)x^3 - 2sinx + 4x + C\nSince f(0) = 2, we have\n(1/3)0^3 - 2sin(0) + 4(0) + C = 2\nC = 2\nSo f(x) = (1/3)x^3 - 2sin(x) + 4x + 2\nTo find f(2) just replace x with 2 and evaluate.\n2.  Find the antiderivative of 7x +4\nIt is f(x) = (7/2)x^2 + 4x + C\nSince it passes through the point (9,5) that means x = 9 and f(x) = 5\n5 = (7/2)9^2 + 4(9) + C\n5 = (7/2)81 + 36 + C\n5 = 567/2 + 36 + C\n5 = 639/2 + C\nC = 5 - 639/2 = -629/2\nThus, f(x) = (7/2)x^2 + 4x - 629/2\nPlug in x = 3 and solve for f(x).
852832
x = [-b +/- sqrt(b^2 - 4ac)] / (2a)\nf(x): a = 1, b = 0, c = -4\ng(x): a = 1, b = -1, c = -12
810099
Use distribution to simplify...\n\n6f + 27 = -7 + f\n\nNow isolate the variable and solve.
821547
f(x)=4x^2 + 9x - 2\n\nhere, this means the function (f) of x=4x^2 + 9x - 2\n\nso if there was f(2)=4x^2 + 9x - 2  that would mean solve the function if x=2
752287
I'd suggest that you draw a picture. The area 'under' the inverse function can also be seen as the area to the *left* of the graph of y=f(x), i.e. x=f^(-1)(y).\n\nThe area under y=f(x) consists of a rectangle bounded by y=2, y=0, x=7 and x=11, and the area under y=f(x) and above y=2 from x=7 to x=11. By subtraction, this second area is 6.787151.\n\nNow the area to the left of y=f(x) consists of a rectangle bounded by y=2, y=5, x=0 and x=7 and the second area above. This gives a total of 21+6.787151=27.787151. This is the answer you seek.