Find the inverse of the function f(x)= (4x-7)/(x-1)
First change f(x) to y=(4x-7)/(x-1), it will be easier in the long run. The first step is to multiply both sides by the term (x-1): y*(x-1)=((4x-7)/(x-1))*(x-1) Distribute and cancel any possible terms yx-y=4x-7 Now subtract 4x from both sides yx-y-4x=-7 Add y to both sides yx-4x=y-7 Factor out the x x(y-4)=y-7 Divide both sides by (y-4), this gives the inverse of the f(x)=(4x-7)/(x-1) x=(y-7)/(y-4)
Find the molar mass of C12H22O11 (table sugar).
In order to find the molar mass of any compound, a periodic table is needed. Given the molar masses of each atom: C=12.01 g/mol H=1.00 O=15.99 g/mol. Now, because there are 12 carbon atoms, we multiply 12.01*12, giving 144.1 g/mol, 22 hydrogen atoms, multiply 1.00*22, giving 22.00 g/mol, and 11 oxygen atoms, multiply 15.99*11, giving 175.9 g/mol. The last step is to simply add all of these values for an overall molar mass of 144.1+22.00+175.9=342.00 g/mol C12H22O11
Solve this equation for x: 3x^2=4x^2+84
In order to solve this equation, one must first get all the variables on the same side, this can be done by either subtracting 4x^2 from 3x^2, or the reverse. It is easier in the long run to do the former, so: (3x^2)-(4x^2)=84, which gives -x^2=84. Now divide each side by negative one. x^2=-84 The final step is to take the square root of each side, giving the x-value of x=sqrt(-84) or 84*i.