Problem

Given the functions \(f(x) = \sqrt{x+2}\) and \(g(x) = \frac{1}{x-3}\), find the domain of the sum of the functions \(f(x) + g(x)\).

Answer

Expert–verified
Hide Steps
Answer

The combined domain is the intersection of the two separate domains, which is \(x \geq -2\) and \(x \neq 3\).

Steps

Step 1 ：Step 1: Find the domain of each function separately.

Step 2 ：For \(f(x) = \sqrt{x+2}\), the domain is \(x \geq -2\) because the expression under the square root must be greater than or equal to 0.

Step 3 ：For \(g(x) = \frac{1}{x-3}\), the domain is \(x \neq 3\) because the denominator of a fraction cannot be 0.

Step 4 ：Step 2: Combine the two domains.

Step 5 ：The combined domain is the intersection of the two separate domains, which is \(x \geq -2\) and \(x \neq 3\).

link_gpt

Popular Problems

Compute $\int_{0}^{\ln (2) / … Solve the triangle. \[ \mathr… QUESTION 2 - 1 POINT Solve th… 5. Suppose you are a computer… Answer the statistical measur… $(-\infty, 2) \cap(-6, \infty… A firm does not pay a dividen… Math 112 Section: 4. Tubercul… Find $y^{\prime}$ if $y=\ln \… 3. (3pts) Cherry trees in a c… More