A function f(x) satisfies 2f(x)+3f(1-x)=x^2.… | GMAT Sprint

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PS · Problem Solving

705-805

Functions

A function $f(x)$ satisfies $2f(x)+3f(1-x)=x^2.$ What is the expression of $f(x)$ ?

Correct answer marked below

\frac{(x^2 +6x +3)}{7}

\frac{(x^2 -6x +3)}{7}

\frac{(x^2 -6x +1)}{3}

\frac{(x^2 -6x +3)}{5}

Correct

\frac{(x^2 +6x +3)}{5}

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Explanation

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Official Explanation

Official

We have

2f(x)+3f(1-x)=x^2

... (1)

Substitute

x=1-x

into (1):

2f(1-x)+3f(x)=(1-x)^2

... (2)

Multiply equation (1) by 2 and equation (2) by 3:

4f(x)+6f(1-x)=2x^2

6f(1-x)+9f(x)=3(1-x)^2

Subtract the first resulting equation from the second:…

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What this question tests

Your ability to evaluate and compose functions, including unusual defined operations.

Applying function operations in the wrong order or ignoring domain restrictions.