The domain of the function f(x)=√ log 10((5 x-x2/4)) is

Question

The domain of the function f(x)=√ log 10((5 x-x2/4)) is (A) [0,1] (B) [1,4] (C) [4,5] (D) [-∞, ∞]

Tardigrade Admin · Accepted Answer

We have f(x)=√ log 10((5 x-x2/4)) For f(x) to be defined ⇒ (5 x-x2/4) ≥ 1 and (5 x-x2/4)>0 ⇒ (5 x-x2/4) ≥ 1 ⇒ 5 x-x2 ≥ 4 ⇒ x2-5 x+4 ≤ 0 ⇒ (x-4)(x-1) ≤ 0 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/a149ad1ecd27ef35ec73971b3435a743-.png" /> ∴ x ∈[1,4] So, domain of f(x) is [1,4

Q. The domain of the function $f (x) = lo g_{10} (\frac{5 x - x ^{2}}{4})$ is

$[0, 1]$

$[1, 4]$

$[4, 5]$

$[- \infty, \infty]$

Q. The domain of the function f(x)=log10​(45x−x2​)​ is

[0,1]

[1,4]

[4,5]

[−∞,∞]

We have f(x)=log10​(45x−x2​)​ For f(x) to be defined ⇒45x−x2​≥1and 45x−x2​>0 ⇒45x−x2​≥1 ⇒5x−x2≥4 ⇒x2−5x+4≤0 ⇒(x−4)(x−1)≤0 ∴x∈[1,4] So, domain of f(x) is [1,4}

Q. The domain of the function $f (x) = lo g_{10} (\frac{5 x - x ^{2}}{4})$ is

$[0, 1]$

$[1, 4]$

$[4, 5]$

$[- \infty, \infty]$