Topic 6 of 6
Radicals, Exponents & Functions
Move between radical and exponent notation, solve carefully, and use function language to describe inputs, outputs, and inverses.
01Algebra · Method guideSimplifying radicals by pulling out perfect powersFactor the radicand into a perfect power times what remains. Pull only complete groups through the radical bar.02Algebra · Method guideSolving radical equations and checking for extraneous rootsIsolate one radical, raise both sides to the matching power, solve, and check every candidate in the original equation.03Algebra · Concept explainerRational exponents: the bridge between powers and rootsThe denominator names the root and the numerator names the power. This notation lets radical expressions use the ordinary exponent rules.04Algebra · Concept explainerFunction notation: inputs, outputs, and what f(x) does not meanf(x) names the output of function f at input x. The parentheses indicate evaluation, not multiplication.05Algebra · Decision guideInverse function or reciprocal? The −1 notation has two different jobsf⁻¹ reverses a function's input-output pairing; 1/f takes reciprocal outputs. They are generally different operations.