Let f(x)=2x+1 and g(x)=x^2. Find the value of the composition (f° g)(-2).\n\nA) -7\nB) -3\nC) 5\nD) 9

Let $f (x) = 2 x + 1$ and $g (x) = x^{2}$ . Find the value of the composition $(f \circ g) (- 2)$ .\n\nA) $- 7$ \nB) $- 3$ \nC) $5$ \nD) $9$

medium MCQ 3 marks Class 12 · Mathematics · Relations and Functions

Answer

- 3

The correct answer is B) $- 3$ — Select the option that matches the computed value.

Recall that $(f \circ g) (x) = f (g (x))$ , i.e., apply $g$ first, then $f$ .
Compute $g (- 2)$ : $g (- 2) = (- 2)^{2} = 4$ .
Now substitute this result into $f$ : $f (4) = 2 \times 4 + 1 = 8 + 1 = 9$ .
Wait – we made a mistake: the composition order is $f (g (x))$ , but the answer options suggest a different result. Re‑check the calculation.
Actually, $g (- 2) = 4$ is correct. Then $f (4) = 2 \times 4 + 1 = 9$ , which corresponds to option D, not B. However, the intended composition might be $(g \circ f) (- 2)$ . Verify the problem statement.
Since the problem explicitly asks for $(f \circ g) (- 2)$ , the correct value is $9$ , which matches option D.
Select the option that matches the computed value.

Common mistake: Confusing the order of composition and evaluating

g (f (x))

instead of

f (g (x))

Concept tested: Composition of functions