(A) 7/2

(B) −25/6

(C) 25/6

(D) −7/2

Correct Answer: 7/2

Explanation

Given:

g(x) = 3x² + 2x − 3

So,

g(f(x)) = 3[f(x)]² + 2f(x) − 3

From the question:

4g(f(x)) = 3x² − 32x + 72

Divide both sides by 4:

g(f(x)) = 3/4 x² − 8x + 18

Comparing,

3[f(x)]² + 2f(x) − 3 = 3/4 x² − 8x + 18

Solving this quadratic relation, we get:

f(x) = x/2 − 3

Now verify using f(0) = −3 (satisfied).

Compute g(2):

g(2) = 3(2)² + 2(2) − 3 = 12 + 4 − 3 = 13

Now,

f(g(2)) = f(13) = 13/2 − 3 = 7/2

Hence, the required value is 7/2.

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