Question

If \(f(x) = x^2\) and \(g(x) = [x^2]\) where \([\cdot ]\) represents the greatest integer function then, \((f\circ g)(\frac{3}{2})+(g\circ f)(\frac{3}{2})\) is equal to ...

• A. \(2\)
• B. \(5\)
• C. \(9\)
• D. \(10\)

Hint:

Compute each composite carefully, applying the inner function first.

Answer 1

The Correct Option is C

Step 1: Table of Values:
At $x=1.5$: $x^2=2.25$, so $g=2$ and $f=2.25$.

Step 2: Composites:
$f(g)=f(2)=4$. For $g(f)$, apply $g$ to 2.25: $2.25^2=5.0625$ and the greatest integer is 5.

Step 3: Total:
$4+5=9$. Option (C).

Final Answer:
Option (C). \[ \boxed{\text{(C) } 9} \]