Suppose that f is continuous at x 5 and that g is continuou

Suppose that f is continuous at x = 5 and that g is continuous at x = 8. Also suppose that f(5) = 8 and g(8) = 10. What is lim g(f(x))? Why? ( That is explain what theorems you are using to get your answer). x5

Solution

Given that f is continuous at x =5 and g at x=8

g(8) =10

Hence g{f(x)} = g{f(5)} when x =5

= g(8) = 10

Hence limit x tends to 5 of gof(x) =10