Q67 / 160 · TS EAMCET 2015 · Mathematics

If $f(x)$ is a real function defined on $[-1,1]$, then the function $g(x)=f(5 x+4)$ is defined on the interval

  • A
    $[-4,9]$
  • Correct answer
    B
    $-\frac{3}{5}$
  • C
    $[-2,9]$
  • D
    $[-3,9]$

Solution

$\because$ Real function $f(x)$ defined on $[-1,1]$. $$ \begin{aligned} & \therefore \quad f(5 x+4)=g(x) \text { defined for } \\ & -1 \leq 5 x+4 \leq 1 \\ & \Rightarrow \quad-5 \leq 5 x \leq-3 \quad \text { [adding }-4 \text { in each term] } \\ & \Rightarrow \quad-1 \leq x \leq \frac{-3}{5} \\ & \text { [dividing each term by 5] } \\ & \Rightarrow \quad x \in\left[-1, \frac{-3}{5}\right] \\ & \end{aligned} $$

Hence, the correct answer is option: 'B'.

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