How do you find the compositions given #f(x)=-3x+5#, #g(x)=1+2x-x^2#?

1 Answer
Noah G
Feb 10, 2016

There are many compositions possible. I'll give you one: #ƒ(g(x))#

Explanation:

#ƒ(g(x))# means to plug function g into function ƒ. The function on the inside is always to be plugged into the function on the outside. This can also be notated #(ƒ @ g)(x) #, which is read inside to outside as well. When a number is written in place of x, it means to use the number as the value of x in the inner function, which will give you a numerical result. Afterwards, you plug that number into x in the outer function.

#ƒ(g(x))# = #ƒ(-x^2 + 2x + 1)#

= #-3(-x^2 + 2x + 1) + 5#

=#3x^2 - 6x - 3 + 5#

=#3x^2 - 6x + 2#

So, #ƒ(g(x)) = 3x^2 - 6x + 2#

Practice exercises:

  1. Assuming #ƒ(x) = 1/(3x - 4)# and #g(x) = 3x^2 - 6#.

Find the following compositions:

a) #g(ƒ(x))#

b) #ƒ(g(-4))#

Good luck!

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