X H 5. Given f (x) = 2x g(x) = x + 4 and h(x) = 5 – x 3 find (f + g)(2) (h – g)(2) (f × h)(2) and (h / g)(2) This exercise differs from the previous one in that I not only have to do the operations with the functions but I also have to evaluate at.
To find f (x+h) substitute x = x + h into the function f (x +h) = (x +h)2 − 2(x +h) +5 now distribute the brackets f (x +h) = x2 + 2hx +h2 − 2x − 2h +5 which may be expressed as f (x +h) = x2 + 2x(h −1) +h2 − 2h +5 Answer link.
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DomainsDomain of Composite FunctionWhy Both Domains?DeComposing FunctionIt has been easy so far but now we must consider the Domainsof the functions The domain is the set of all the valuesthat go into a function The function must work for all values we give it so it is up to usto make sure we get the domain correct! It is important to get the Domain right or we will get bad results! We must get both Domains right (the composed function andthe first function used) When doing for example (g º f)(x) = g(f(x)) 1 Make sure we get the Domain for f(x)right 2 Then also make sure that g(x)gets the correct Domain Well imagine the functions are machines the first one melts a hole with a flame (only for metal) the second one drills the hole a little bigger (works on wood or metal) So what happens “inside the machine” is important We can go the other way and break up a functioninto a composition of other functions This can be useful if the original function is too complicated to work on.
How do you find f(x+h) for the function f(x)= x^2 2x + 5
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