to find the inverse "relation" of any equation, simply do a switcharoo on the variables, now, if the resulting inverse "relation" happens to be a function, as the "vertical line test" has it, then is also an "inverse function" and as 3a said it, yes, only one-to-one functions have inverse functions
so let's see Numliters(t) then
[tex]\bf Numliters(t)=\boxed{y}=354+8(\boxed{t}-62)
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inverse\implies \boxed{t}=354+8(\boxed{y}-62)
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\textit{and now, let's solve for "y"}
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t-354=8(y-62)\implies \cfrac{t-354}{8}=y-62
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\cfrac{t-354}{8}+62=y=f^{-1}(t)
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\textit{now, you're asked to call it "temp"}
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\cfrac{t-354}{8}+62=Temp(t)[/tex]
now, name wise, heck, you can call it whatever you want, even spaghetti
[tex]\bf \cfrac{t-354}{8}+62=spaghetti(t)[/tex]
anyhow...that's the inverse function
