SOLUTION: Can you step me through this process? Given the two functions r(t) = 3t + 4 and t(s) = 2s - 5, write r as a function of s.

Algebra ->  Functions -> SOLUTION: Can you step me through this process? Given the two functions r(t) = 3t + 4 and t(s) = 2s - 5, write r as a function of s.      Log On


   

Question 172782: Can you step me through this process?
Given the two functions r(t) = 3t + 4 and t(s) = 2s - 5, write r as a function of s.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
You are given r as a function of t and t as a function of s. So what you need to do to find r as a function of s is to plug in the value of t on the right side of r(t)
t%28s%29+=+2s+-+5
r%28t%29+=+3t+%2B+4
r%28s%29+=+3%282s+-+5%29+%2B+4
r%28s%29+=+6s+-15+%2B+4
r%28s%29+=+6s+-+11
Now try out a sample value to see that it works.
Let s=2
Then t%282%29+=+2%2A2+-+5
t%282%29+=+4+-+5
t%282%29+=+-1
Now use the value we got for t as input to r(t)
r%28-1%29+=+3%28-1%29+%2B+4
r%28-1%29+=+-3+%2B+4+
r%28-1%29+=+1 so, when s = 2, r = 1
Now use the equation we made
r%28s%29+=+6s+-+11
r%282%29+=+6%2A2+-+11
r%282%29+=+12+-11
r%282%29+=+1 and again, when s=2 r = 1
So it works!