Let-f-x-is-a-quadratic-equation-and-x-2-2x-3-f-x-2x-2-4x-4-for-every-x-R-If-f-5-26-then-f-7-is-equal-to-A-38-D-74-B-50-E-92-C-56-

Question Number 21692 by Joel577 last updated on 01/Oct/17

Let f (x) is a quadratic equation and

x^{2} - 2 x + 3 ⩽ f (x) ⩽ 2 x^{2} - 4 x + 4

for every x \in R

If f (5) = 26, then f (7) is equal to \dots

(A) 38 (D) 74

(B) 50 (E) 92

(C) 56

Answered by mrW1 last updated on 01/Oct/17

x^{2} - 2 x + 3 = {(x - 1)}^{2} + 2

{2 x}^{2} - 4 x + 4 = 2 {(x - 1)}^{2} + 2

let f (x) = a {(x - 1)}^{2} + 2 with 1 ⩽ a ⩽ 2

f (5) = a {(5 - 1)}^{2} + 2 = 26

\Rightarrow a = \frac{3}{2}

\Rightarrow f (7) = \frac{3}{2} {(7 - 1)}^{2} + 2 = 3 \times 18 + 2 = 56

Answer (C)

Commented by Joel577 last updated on 01/Oct/17

t h a n k y o u v e r y m u c h

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