From x=(7y-1+3)/(5y-1+7) multiply both sides by (5y-1+7) to get;
x(5y-1+7) = 7y-1+3 Now distribute the x in to the parentheses on the left hand side:
5xy-1 + 7x = 7y-1+3 Subtract 5xy-1 from both sides:
7x = 7y-1+3 - 5xy-1 Subtract 3 from both sides:
7x - 3 = 7y-1 - 5xy-1 Factor the right hand side:
7x - 3 = (7 - 5x)y-1 Divide both sides by 7 - 5x:
(7x - 3)/(7 - 5x) = y-1
or y-1 = (7x - 3)/(7 - 5x)
(Note that the original function is not defined at x = -7/5, so there is no inverse at this point; and the inverse function isn't defined at x = +7/5).
And this has been answered here: https://web2.0calc.com/questions/help_46851
Please don't ask the same question without checking if it had an answer the first time you asked it!
If you didn't understand the first answer, say so as a continuation of the same thread rather than starting a new one (and try to explain just what you didn't understand).
1. The solid heats up by 40 degC in 5 minutes, so that's 8 degC/minute
The liquid heats up by 48 degC in (21.6 - 12) minutes, so that's 5 degC/minute.
(I've assumed that by "substance" you are referring to the totally liquid phase).
2. If the same rate of heat input is used then for twice the material, the positive slopes for the solid and liquid phases will be half what they are now, and the horizontal, two-phase section will be twice as long. So the solid line will go from 20 C at 0 minutes to 60 C at 10 minutes. The horizontal line will stretch from 10 minutes to 24 minutes. The liquid line will go from 60 degC at 24 minutes to 108 degC at ... minutes. (I'll leave you to work out the ... time).