First slide

Functions (XII)

Question

The domain of the function $f (x) = {[\log_{10} (\frac{5 x - x^{2}}{4})]}^{1 / 2}$ is

Easy

A

$\begin{array}{l} - \infty < x < 8 \end{array}$
B

$\begin{array}{l} 1 \leq x \leq 4 \end{array}$
C

$\begin{array}{l} 4 \leq x \leq 16 \end{array}$
D

$- 1 \leq x \leq 1$

Solution

We have $f (x) = {[\log_{10} (\frac{5 x - x^{2}}{4})]}^{1 / 2}$
From ( 1), clearly, f (x) is defined for those values of x for which
$\log_{10} [\frac{5 x - x^{2}}{4}] \geq 0$
$or (\frac{5 x - x^{2}}{4}) \geq 10^{0}$
$or (\frac{5 x - x^{2}}{4}) \geq 1$
or $x^{2} - 5 x + 4 \leq 0$
or $(x - 1) (x - 4) \leq 0$
Hence, the domain of the function is [1,4].

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