The number of integers- for which the function fx-sin -1-log 2x4- is defined- is equal to

F(x)=sin ^ 1[log _2(x4)] is defined if 1 ≤log _2(x4) ≤ 1 ⇒12≤x4≤ 2 ⇒ 2 ≤ x ≤ 8 Also, x4 gt;0⇒ x gt;0 ∴ x=2,3,4,5,6,7,8 Hence, total 7 integers are there ...

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Standard XII

Mathematics

Rational Function

The number of...

Question

The number of integers, for which the function $f (x) = {sin}^{- 1} [{log}_{2} (\frac{x}{4})]$ is defined, is equal to

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Solution

$f (x) = {sin}^{- 1} [{log}_{2} (\frac{x}{4})]$ is defined if
$- 1 \leq {log}_{2} (\frac{x}{4}) \leq 1 \Rightarrow \frac{1}{2} \leq \frac{x}{4} \leq 2 \Rightarrow 2 \leq x \leq 8$

Also, $\frac{x}{4} > 0 \Rightarrow x > 0$
$∴ x = 2, 3, 4, 5, 6, 7, 8$
Hence, total $7$ integers are there.

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The number of integers, for which the function f(x)=sin−1[log2(x4)] is defined, is equal to

f(x)=sin−1[log2(x4)] is defined if −1≤log2(x4)≤1⇒12≤x4≤2⇒2≤x≤8 Also, x4>0⇒x>0 ∴x=2,3,4,5,6,7,8 Hence, total 7 integers are there.

The number of integers, for which the function $f (x) = {sin}^{- 1} [{log}_{2} (\frac{x}{4})]$ is defined, is equal to

$f (x) = {sin}^{- 1} [{log}_{2} (\frac{x}{4})]$ is defined if
$- 1 \leq {log}_{2} (\frac{x}{4}) \leq 1 \Rightarrow \frac{1}{2} \leq \frac{x}{4} \leq 2 \Rightarrow 2 \leq x \leq 8$

Also, $\frac{x}{4} > 0 \Rightarrow x > 0$
$∴ x = 2, 3, 4, 5, 6, 7, 8$
Hence, total $7$ integers are there.