If f(x)=3-x,-4 le x le 4, then the domain of log e (f (x)) is

Question

If f(x)=3-x,-4 le x le 4, then the domain of log e (f (x)) is (A)  [-4, 4]  (B)  (- ∞ , 3]  (C)  (- ∞ , 3)  (D)  [-4, 3)

Tardigrade Admin · Accepted Answer

Given, f(x)=3-x, -4 le x le 4 Now, log e f (x) =loge (3-x) Here, existance for the above function 3-x>0 ⇒ x-3<0 ⇒ x<3 So, the domain of log e f (x) is (-∞ , 3).

Q. If $f (x) = 3 - x, - 4 \leq x \leq 4,$ then the domain of $lo g_{e} (f (x))$ is

$[- 4, 4]$

$(- \infty, 3]$

$(- \infty, 3)$

$[- 4, 3)$

Given, $f (x) = 3 - x, - 4 \leq x \leq 4$
Now, $lo g_{e} f {(x)} = l o g_{e} (3 - x)$
Here, existance for the above function $3 - x > 0$
$\Rightarrow$ $x - 3 < 0$
$\Rightarrow$ $x < 3$
So, the domain of $lo g_{e} {f (x)}$ is $(- \infty, 3) .$

Q. If f(x)=3−x,−4≤x≤4, then the domain of loge​(f(x)) is

[−4,4]

(−∞,3]

(−∞,3)

[−4,3)