Question

find the inverse of 42t+1550

Answer 1

lets use a symbol to represent the result of the function given:\[y=42t+1550\]this means, given a value for 't', we can use the formulae to get a value for 'y'.
what the question is asking is, given a value for 'y', what value of 't' generated that value for 'y'.

Answer 2

so we need to rearrange the equation so that we have it in the form t=f(y)

Answer 3

so 1st substract 1550 from both sides to get:\[y-1550=42t\]next, divide both sides by 42 to get:\[\frac{y-1550}{42}=t\]now swap left and right sides:\[t=\frac{y-1550}{42}\]

Answer 4

and how would i prove they are inverses?

Answer 5

the standard then is to swap the 'y' and 't' variables to get the inverse function as:\[y=\frac{t-1550}{42}\]

Answer 6

you have two functions:\[y=42t+1550\]and\[y^{-1}=\frac{t-1550}{42}\]
sorry I had missed the inverse operator on the y in the previous step - this is how you show it to be an inverse function.

Answer 7

to prove they are inverses of one another...

Answer 8

you can take the expression for 'y' from the 1st equation and put it in the second equation in place of all the places where you see 't', e.g.:\[y^{-1}=\frac{t-1550}{42}=\frac{(42t+1550)-1550}{42}=\frac{42t}{42}=t\]

Answer 9

so sticking the value for y into \(y^{-1}\) gives you the value of 't' - which is the value that was used to generate 'y'. hence \(y^{-1}\) is the inverse of y.

Answer 10

thank you

Answer 11

yw

Answer 12

how would i graph the inverse?

Answer 13

the inverse we found was:\[y^{-1}=\frac{t-1550}{42}=\frac{t}{42}-36\frac{19}{21}\]so this is just a straight line with slope \(\frac{1}{42}\) and y intercept at \(-36\frac{19}{21}\)