How do you find the composition of function given f(x)= sqrt (x+8)f(x)=√x+8 and g(x)= 4x + 1g(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))f(g(x)), you must plug function g into f.

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

f(g(x)) = sqrt(4x + 9f(g(x))=√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)))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^xa(x)=2x2−8x+6,b(x)=2x+3andc(x)=2x. Find:

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

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

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

d). a(b(c(-2))a(b(c(−2))

Challenge problem:

Find two functions, f(x) and g(x)f(x)andg(x), if their compositions give 2/(2x - 1)^22(2x−1)2

Good luck!

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