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