Domain of a Function - Algebra Step by Step

Find the domain of f(x)=√(x-3): require x-3≥0, so x≥3. Evaluate f(7)=√(7-3)=√4=2.

Example

Use the square-root restriction to find the domain, then evaluate.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

f(x)= \sqrt{x- 3 }

Step 2 — Domain condition

For a square root, require x - 3 to be at least 0.

x- \hl{3} \ge \hl{0}

Step 3 — Domain

Solve the restriction: x must be at least 3.

x\ge \hl{3}

Step 4 — Substitute input

Substitute 7: 7 - 3 = 4 under the radical.

f( 7 )=\sqrt{ 7 - 3 }= \hlmath{\sqrt{4}}

Step 5 — Result

Evaluate the square root: f(7) = 2.

f( 7 )= \hl{2}

evaluate-and-domain The domain is the set of all inputs for which the function is defined. For square roots, the radicand must be ≥0. For rational functions, denominators must be ≠0.