The range of the function fx-4-x2-10 x-25 isA- -4- -B- -4- - - 5-D- - 4-

The correct option is D ( ∞,4]f(x)=4 √(x^2 10x+25) ⇒ f(x)=4 √((x 5)^2) ⇒ nbsp;f(x)=4 |x 5| We know that, |x 5| lies from [0,∞) ∴ |x 5| lies in ( ∞,0] Add ...

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Standard XII

Mathematics

Modulus Function

The range of ...

Question

The range of the function $f (x) = 4 - \sqrt{x^{2} - 10 x + 25}$ is

(- \infty, 4]

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[- 4, \infty)

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(- \infty, 5]

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[4, \infty)

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Solution

The correct option is A $(- \infty, 4]$
$f (x) = 4 - \sqrt{x^{2} - 10 x + 25} \Rightarrow f (x) = 4 - \sqrt{(x - 5)^{2}} \Rightarrow f (x) = 4 - | x - 5 |$

We know that, $| x - 5 |$ lies from $[0, \infty)$
$∴ - | x - 5 |$ lies in $(- \infty, 0]$

Adding $4$ , we get

Graph will get shifted upwards by $4$ units
$∴$ Range of $f (x)$ is $(- \infty, 4]$

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Modulus Function

Standard XII Mathematics

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The range of the function f(x)=4−√x2−10x+25 is

The correct option is A (−∞,4]f(x)=4−√x2−10x+25⇒f(x)=4−√(x−5)2⇒f(x)=4−|x−5| We know that, |x−5| lies from [0,∞) ∴−|x−5| lies in (−∞,0] Adding 4, we get Graph will get shifted upwards by 4 units ∴ Range of f(x) is (−∞,4]

The range of the function $f (x) = 4 - \sqrt{x^{2} - 10 x + 25}$ is