How do you find (f of g of h) if #f(x)=x^2+1# #g(x)=2x# and #h(x)=x-1#?
1 Answer
Mar 4, 2018
Explanation:
Given:
#{ (f(x) = x^2+1), (g(x) = 2x), (h(x) = x-1) :}#
One way of thinking about these function compositions is to go back and forth between the symbols and verbal descriptions of what the functions do.
In our example:
-
#f# takes the square of a number and adds#1# -
#g# doubles a number -
#h# subtracts#1# from a number
So a verbal description of the composed
-
Subtract
#1# -
Double
-
Square
-
Add
#1#
So in symbols we might describe this process thus:
#x -> x-1 -> 2(x-1) -> (2(x-1))^2 -> (2(x-1))^2+1#
So:
#(f@g@h)(x) = f(g(h(x)))#
#color(white)((f@g@h)(x)) = (2(x-1))^2+1#
#color(white)((f@g@h)(x)) = 4(x^2-2x+1)+1#
#color(white)((f@g@h)(x)) = 4x^2-8x+4+1#
#color(white)((f@g@h)(x)) = 4x^2-8x+5#
