Evaluating

Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 36 of 43.

A radical function is evaluated like any other: replace x with the input. Take f(x) = √(3x + 1) - 2 and the input 5. Using the rule writes √(3(5) + 1) - 2.

Then work from the inside out. The inside is 3(5) + 1, which is 16, so the next line is √(16) - 2. Only now take the root: the square root of 16 is 4, which leaves 4 - 2, and f(5) is 2.

The root waits for the inside because it covers all of it. It does not split over a sum: √(9 + 16) is √(25), which is 5, not 3 plus 4. An input outside the domain shows up at once: f(-1) puts √(-2) on the board, which has no real value.

Challenge

Use f(x) = √(2x + 3) - 1 to work out f(11). Tap the move that uses the rule, then type each next line in the box and press Enter: work out the inside first, then the root. The board accepts a line only when its value equals the line above.

Try it yourself

f(11)

Simplify the expression