The range of the function fx-4-x2-10x-25 is

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] Adding 4, we get Graph will get ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

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]

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

[- 4, \infty)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(- \infty, 5]

No worries! We‘ve got your back. Try BYJU‘S free classes today!

[4, \infty)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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 $(- \infty, 4]$

Suggest Corrections

Similar questions

Q. The range of the function

f (x) = 4 - \sqrt{x^{2} - 10 x + 25}

Q. The range of the function

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

Q. Find the domain and range of the function

f (x) = \sqrt{x^{2} - 25}

and

f (x) = \sqrt{25 - x^{2}}

Q. Find the domain and range of the real function

f (x) = \sqrt{25 - x^{2}}

Q. The range of the function

f (x) = (\frac{x^{2} + 8}{x^{2} + 4}), x \in R

Join BYJU'S Learning Program

Explore more

Modulus Function

Standard XII Mathematics

Join BYJU'S Learning Program

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