How do you find the composition of function given #f(x)= sqrt (x+8)# and #g(x)= 4x + 1#?

1 Answer
Noah G
Mar 6, 2016

There are many different compositions possible. I'll show you one.

Explanation:

To complete a function composition, you must substitute one function in the place of x in the other. For example in #f(g(x))#, you must plug function g into f.

#f(g(x)) = sqrt((4x + 1) + 8#

#f(g(x)) = sqrt(4x + 9#

When finding the composition of functions think of working from the inside to the outside. So, if you have #f(g(h(x)))#, you plug h into g and then you plug the result from that calculation. When there is a number in the place of x, you must plug that number in for x and then work your way out.

Practice exercises:

  1. Assuming functions #a(x) = 2x^2 - 8x + 6, b(x) =2x + 3 and c(x) = 2^x#. Find:

a). #c(a(b(x))#

b). #a(b(c(x))#

c). #b(c(b(3))#

d). #a(b(c(-2))#

Challenge problem:

Find two functions, #f(x) and g(x)#, if their compositions give #2/(2x - 1)^2#

Good luck!

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