If f(x) = x2 – 2x and g(x) = 2x + 3, then the minimum value of f(g(x)) - 2x is
Explanation:
f(g(x)) = (2x + 3)2 – 2x
⇒ f(g(x)) - 2x = (2x + 3)2 – 2x - 2x
⇒ f(g(x)) - 2x = 4x2 + 8x + 9
The given expression is quadratic. The least value of a quadratic expression ax2 + bx + c occurs at x = - b/2a
∴ Minimum value of f(g(x)) occurs at x = - 8/8 = -1
∴ Minimum value of f(g(x)) is = 4 × (-1)2 + 8 × -1 + 9 = 4 - 8 + 9 = 5
Hence, option (b).
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