negative half power

Practise negative half power with an original VectorPaths question, worked explanation and related VCE Methods practice.

3 practice marks

Original practice question

For the real function $f(x)=4x^{-1/2}$, state the domain and range, then solve $f(x)=1$.

Worked explanation

• Find the real domain

  The square root in the denominator requires $x>0$.

• Find the range

  Every output is positive; it tends to infinity near $0^+$ and to zero as $x\to\infty$. The range is $(0,\infty)$.

• Solve

  $\sqrt x=4$, so $x=16$.

Domain $(0,\infty)$; range $(0,\infty)$; $x=16$.

Original VectorPaths practice; not an official VCAA question or marking rubric.