Question

• If f(x)=4x-x², find
√f(3/2)

Answer 1

`f(x)=4x-x^2\hspace{5em}f\left( (3)/(2) \right)=4\left( (3)/(2) \right)-\left( (3)/(2) \right)^2\implies f\left( (3)/(2) \right)=6-\cfrac{3^2}{2^2} \\\\\\ f\left( (3)/(2) \right)=6-\cfrac{9}{4}\implies f\left( (3)/(2) \right)=\cfrac{24-9}{4}\implies f\left( (3)/(2) \right)=\cfrac{15}{4} \\\\[-0.35em] ~\dotfill\\\\ \sqrt{f\left( (3)/(2) \right)}\implies \sqrt{\cfrac{15}{4}}\implies \cfrac{√(15)}{√(4)}\implies \cfrac{√(15)}{2}`