The range of the expression fx-3 x2-12 x-5 isA- -4- -B- -4-C- -7- -D- None of these

The correct option is C Compare 3x^2 12x + 5 with ax^2 bx + c Here, a gt; 0 ⇒ Minimum value of f(x) occur at x = b/2a and the value is D/4a D = b^ ...

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Standard IX

Mathematics

Using Graph to Find Range of a Function

The range of ...

Question

The range of the expression $f (x) = 3 x^{2} - 12 x + 5$ is

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Solution

The correct option is C

Compare $3 x^{2} - 12 x + 5 w i t h a x^{2} - b x + c$

Here, a > 0 $\Rightarrow$ Minimum value of f(x) occur at $x = \frac{- b}{2 a}$ and the value is $\frac{- D}{4 a}$

$D = b^{2} - 4 a c$

$= {(12)}^{2} - 4 (3) (5)$

Minimum value = $\frac{- 84}{12} = - 7$

As a > 0, graph of f(x) is upward.

As minimum value is -7,

Maximum value extends to $\infty$

So, the range is [-7, $\infty$ )

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The range of the expression f(x)=3x2−12x+5 is

The range of the expression $f (x) = 3 x^{2} - 12 x + 5$ is