Relations and Functions
Xam Idea
CBSE
Grade 12
Question:
Let $f: \mathbb{R} \to \mathbb{R}$ be defined by $f(x) = 2x + 1$ and $g(x) = x^2 - 2$. Find $(g \circ f)(x)$ and $(f \circ g)(x)$.
Step-by-Step Solution
Key Concept: g(f(x)) = (2x+1)^2 - 2 = 4x^2 + 4x - 1. f(g(x)) = 2(x^2-2) + 1 = 2x^2 - 3.
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Correct Answer:
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