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Can sage be used to solve the following kind of problem?

"Given that f(1) = 9, f(1) = 5, g(9) = 6 and g(9) = 4, what is the approximate value of g(f(1.05))?"

Can sage be used to solve the following kind of problem?

"Given that f(1) = 9, f(1) f'(1) = 5, g(9) = 6 and g(9) g'(9) = 4, what is the approximate value of g(f(1.05))?"