Let f and g be real functions defined by f(x) = 2x + 1 and g(x) = 4x - 7.

(i) For what real numbers $x, f (x) = g (x) ?$

(ii) For what real numbers x, f(x) < g(x)

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Solution

Solution

Given :
$f (x) = 2 x + 1 a n d g (x) = 4 x - 7$

To find The value of x for f(x) = g(x)

Get the value of unknown by simplifying the

given equation.

$f (x) = g (x)$

$\Rightarrow 2 x + 1 = 4 x - 7$

$\Rightarrow 2 x = 8$

$\Rightarrow x = 4$

(ii)
Given :
$f (x) = 2 x + 1 a n d g (x) = 4 x - 7$

To find The value of x for f(x) < g(x)

Get the value of unknown by simplifying the

given equation.

$f (x) < g (x)$

$\Rightarrow 2 x + 1 < 4 x - 7$

$\Rightarrow 8 < 2 x$

$\Rightarrow x > 4$

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