Question

For the functions
f(x) = x^2+1
g(x) = (e(x))/(x-1)

Calculate (f ∘ g)(x) & (g ∘ f)(x)
What are the Domains of (f ∘ g)(x) & (g ∘ f)(x)

Answer 1

Answer on Question #52350 – Math – Real Analysis

For the functions

$$f(x) = x^2 + 1$$ $$g(x) = \frac{e^x}{(x - 1)}$$

Calculate $(f \circ g)(x)$ and $(g \circ f)(x)$.

What are the domains of $(f \circ g)(x)$ and $(g \circ f)(x)$?

Solution:

$$(f \circ g)(x) = f(g(x)) = \left(\frac{e^x}{(x - 1)}\right)^2 + 1$$

$(f \circ g)(x)$ is not defined at $x = 1$, as this value would result in division by zero. Hence the domain of $(f \circ g)(x)$ is all real numbers except 1.

$$(g \circ f)(x) = g(f(x)) = \frac{e^{(x^2 + 1)}}{(x^2 + 1 - 1)} = \frac{e^{(x^2 + 1)}}{x^2}$$

$(g \circ f)(x)$ is not defined at $x = 0$, as this value would result in division by zero. Hence the domain of $(f \circ g)(x)$ is all real numbers except 0.

www.AssignmentExpert.com