let f(x)=x2-1x and g(x)=x+8. Evaluate the following

Question

let f(x)=x²-1x and g(x)=x+8. Evaluate the following

f∘g(x)=

g∘f(x)=

f∘f(x)=

g∘g(x)=

Answer 1

This is a function composition problem. The main idea is to plug the entirety of one function, into the other, and then simplify. You can think of this symbol like this:

f∘g(x)= f(g(x))

Let f(x)=x²-x g(x)=x+8.

f∘g(x)= f(g(x)) = f(x+8) = (x+8)²-(x+8) = x²+16x+64 - x - 8 = x²+15x+56

g∘f(x)= g(f(x)) = g(x²-x) = (x²-x)+8 = x²-x+8

f∘f(x)= f(f(x)) = f(x²-x) = (x²-x)²-(x²-x) = x⁴-2x³+x² - x² + x = x⁴-2x³+x

g∘g(x)= g(g(x)) = g(x+8) = (x+8) + 8 = x + 16