Relations And Functions Practice Questions Ques21
Question: The functions are $f(x) = 2x + 1$ and $g(x) = x^2$. Then the value of $(g \circ f)(x)$ is
Options:
(A) $(f \circ g)(x) = 2x^2 + 1$
(B) $(f \circ g)(x) = (2x + 1)^2$
(C) $(g \circ f)(x) = (2x + 1)^2$
(D) $(g \circ f)(x) = 2x^2 + 1$
Show Answer
Answer: C
Explanation:
(A) Incorrect. This is $(f \circ g)(x)$, not $(g \circ f)(x)$.
(B) Incorrect. This is $(g \circ f)(x)$, but the question asks for $(f \circ g)(x)$.
(C) Correct. $(g \circ f)(x) = g(f(x)) = g(2x + 1) = (2x + 1)^2$.
(D) Incorrect. This is not the correct composition of $g$ and $f$.
BETA
