The value of the composite functions (g∘f)(x) and (f∘g)(x) are 32x^2 + 16x + 3 and 8x^2 + 5 respectively
Composite functions
Composite function is also known as function of a function. They are determined by representing x with the other function.
Given the following functions
f(x)=4x+1
g(x)=2x^2+1
(f∘g)(x) = f(g(x))
(f∘g)(x) = f(2x^2+1)
(f∘g)(x) = 4(2x^2+1) + 1
(f∘g)(x) =8x^2 + 5
For the composite function (g∘f)(x)
(g∘f)(x) = g(f(x))
(g∘f)(x) = g(4x+1)
Replace x wit 4x+1 to have:
(g∘f)(x) = 2(4x+1)^2 + 1
(g∘f)(x)= 2(16x^2+8x+1) + 1
(g∘f)(x) = 32x^2 + 16x + 3
Hence the value of the composite functions (g∘f)(x) and (f∘g)(x) are 32x^2 + 16x + 3 and 8x^2 + 5 respectively
Learn more on composite function here: https://brainly.com/question/10687170
#SPJ1
