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

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Vishal Baghel | Contributor-Level 10

2 weeks ago

$f (x) = a x^{2} + b x + c$

g (x) = px + q

$f (g (x)) = a {(p x + q)}^{2} + b (p) (+ q) + c$

$? 8 x^{2} ? 2 x = a {(p x + q)}^{2} + b (p x + q) + c$

Compare 8 = ap² …………… (i)

-2 = a (2pq) + bp

0 = aq² + bq + c

$9 (f (x)) = p (a x^{2} + b x + c) + q$

=>4x² + 6x + 1 = apx² + bpx + cp + q

=> Andhra Pradesh = 4 ……………. (ii)

6 = bp

1 = cp + q

From (i) & (ii), p = 2, q = -1

=> b = 3, c = 1, a = 2

f (x) = 2x² + 3x + 1

f (2) = 8 + 6 + 1 = 15

g (x) = 2x – 1

g (2) = 3

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

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

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