If g(x)=x²+x-2 and 1/2(g f)(x)=2 x²-5 x+2 then f(x) is equal to

Correct Answer is : 2x−32 x-32x−3

Correct Answer is : 2x−32 x-32x−3

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MHTCET 11 Apr 2026 Shift 2 Paper

Question : 118 of 150

Marks: +1, -0

g(x)=x^{2}+x-2

\frac{1}{2}(g \circ f)(x)=2 x^{2}-5 x+2

f(x)

is equal to

Solution:

Concept:

Composite functions and verifying options by substitution.

Explanation:

Given

g(x)=x^{2}+x-2

and

\frac{1}{2}(g \circ f)(x)=2 x^{2}-5 x+2

Multiply both sides by

2

to get

(g \circ f)(x)=4x^{2}-10x+4

Since

g(f(x))=(f(x))^{2}+f(x)-2

, we need

(f(x))^{2}+f(x)-2=4x^{2}-10x+4

Check option B:

f(x)=2x-3

Then

g(f(x))=(2x-3)^{2}+(2x-3)-2

Expand:

4x^{2}-12x+9+2x-3-2=4x^{2}-10x+4

This matches the required expression, so option B is correct.

Answer:

f(x)=2x-3

Correct option: B.

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