JEE Main 2022 · 29 Jun · Shift 2 · Mathematics Q30

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MathematicsInteger+4 / -1Question 30 of 90

Let $f(x)$ and $g(x)$ be two real polynomials of degree 2 and 1 respectively. If $f(g(x))=8x^2-2x$ , and $g(f(x))=4x^2+6x+1$ , then the value of $f(2)+g(2)$ is ______.

Your answer

Answer and worked solution

Official answer: 18

Leading terms. $g=ax+b$ , $f=px^2+qx+r$ : $pa^2=8$ , $ap=4$ , so $a=2$ , $p=2$ .

Match. $g(f)$ : $2q=6$ , $q=3$ , $2r+b=1$ . $f(g)$ : $8b+6=-2$ , $b=-1$ , $r=1$ .

Value. $f(2)=15$ , $g(2)=3$ : 18.

Answer: 18

Topics:Composition and inverse functions Polynomials and remainder theorem

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JEE Main 2022 · 29 Jun · Shift 2, Mathematics question 30