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Let $f$ and $g$ be real functions defined by $f(x)=2 x+1$ and $g$ $(x)=4 x-7$.
(i) For what real number $x, f(x)=g(x)$ ?
(ii) For what real number $x, f(x) < g(x)$ ?
(i) For what real number $x, f(x)=g(x)$ ?
(ii) For what real number $x, f(x) < g(x)$ ?
Solution:
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Verified Answer
We have, $f(x)=2 x+1$ and $g(x)=4 x-7$
(i) for $f(x)=g(x)$
$\Rightarrow 2 x+1=4 x-7 \Rightarrow 2 x=8 \Rightarrow x=4$
(ii) For $f(x) < g(x)$
$$
\begin{aligned}
&\Rightarrow 2 x+1 < 4 x-7 \\
&\Rightarrow-2 x+1 < -7 \quad \Rightarrow \quad-2 x < -7-1 \\
&\Rightarrow-2 x < -8 \quad \therefore x>4
\end{aligned}
$$
(i) for $f(x)=g(x)$
$\Rightarrow 2 x+1=4 x-7 \Rightarrow 2 x=8 \Rightarrow x=4$
(ii) For $f(x) < g(x)$
$$
\begin{aligned}
&\Rightarrow 2 x+1 < 4 x-7 \\
&\Rightarrow-2 x+1 < -7 \quad \Rightarrow \quad-2 x < -7-1 \\
&\Rightarrow-2 x < -8 \quad \therefore x>4
\end{aligned}
$$
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