Answer:
Step-by-step explanation:
To find the value of (g ∘ h)(3), we need to first compose the functions g and h, and then evaluate the resulting composite function at x = 3.
Given:
f(x) = 2x + 1
g(x) = 1/(x² + 1)
h(x) = √(x² + 1)
Step 1: Compose the functions g and h.
(g ∘ h)(x) = g(h(x))
(g ∘ h)(x) = 1/(h(x)² + 1)
(g ∘ h)(x) = 1/((√(x² + 1))² + 1)
(g ∘ h)(x) = 1/(x² + 1 + 1)
(g ∘ h)(x) = 1/(x² + 2)
Step 2: Evaluate the composite function (g ∘ h)(x) at x = 3.
(g ∘ h)(3) = 1/(3² + 2)
(g ∘ h)(3) = 1/(9 + 2)
(g ∘ h)(3) = 1/11
Therefore, the value of (g ∘ h)(3) is 1/11.
