AP EAMCET · Maths · Functions
If \(f: R \rightarrow R\) and \(g: R \rightarrow R\) are two functions defined by \(f(x)=2 x-3\) and \(g(x)=5 x^2-2\), then the least value of the function \((g \circ f)(x)\) is
- A \(-2\)
- B \(2\)
- C \(-4\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(-2\)
Step-by-step Solution
Detailed explanation
\((g \circ f)(x) = g(f(x))\) \(= g(2x-3)\) \(= 5(2x-3)^2 - 2\) \(= 5(4x^2 - 12x + 9) - 2\) \(= 20x^2 - 60x + 45 - 2\) \(= 20x^2 - 60x + 43\) The vertex of a parabola \(ax^2+bx+c\) is at \(x = -\frac{b}{2a}\). \(x = -\frac{-60}{2(20)} = \frac{60}{40} = \frac{3}{2}\) Least value…
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