φ*x=φ*f(x)=f(φ(x))=φ(x)=e^x
The book I'm using asks:
Let φ : R → R be given by φ(t) = e^{t} . Let x be the usual coordinate function on R. Show that φ^{*}x = e^{x} .
I can't figure this out and I don't understand why - what is the 'usual coordinate function' on R? I at first interpreted it as f(x) = x, but that doesn't make sense:
f : R → R given by f(x) = x. Then composing f with φ (the definition of pullback) gives φ^{*}x = f(φ(t)) = e^{t}
Am I just doing something very stupid here?