If $f(x) = \sqrt{x}$ and $g(x) = 2x - 3$, find domain of $(f \circ g)(x)$ and $(g \circ f)(x)$.
Step-by-Step Solution
$(f \circ g)(x) = \sqrt{2x-3} \Rightarrow x \ge 3/2 \Rightarrow$ Domain $[3/2, \infty)$. [1.5 Marks]
$(g \circ f)(x) = 2\sqrt{x}-3 \Rightarrow x \ge 0 \Rightarrow$ Domain $[0, \infty)$. [1.5 Marks]
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🎯 Official CBSE Marking Scheme:
Evaluating domain of $(f \circ g) = [3/2, \infty)$: 1.5 Marks
Evaluating domain of $(g \circ f) = [0, \infty)$: 1.5 Marks
Correct Answer: