Let f be continuous on an interval I, and g be continuous on f(I).Show that the composition function g o f defined for x ∈ I by g o f(x) = g(f(x)) is continuous on I.

Let f be continuous on an interval I, and g be continuous on f(I).Show that the composition function g o f defined for x ∈ I by g o f(x) = g(f(x)) is continuous on I.

I am unsure of how exactly I should approach this. I was thinking of obviously using the definition of continuity (using epsilon and delta > 0); however, I am finding myself getting lost in too many variables that don’t really seem to correlate with one another. Any ideas as to how to approach this?

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