Let f and g be real functions defined by

Solution:

According to the question,

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

(a) For what real numbers x, f (x) = g (x)

To satisfy the condition f(x) = g(x),

Should also satisfy,

2x + 1 = 4x–7

⇒ 7 + 1 = 4x–2x

⇒ 8 = 2x

Or, 2x = 8

⇒ x = 4

Hence, we get,

For x = 4, f (x) = g (x)

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

To satisfy the condition f(x) < g(x),

Should also satisfy,

2x + 1 < 4x–7

⇒ 7 + 1 < 4x–2x

⇒ 8 < 2x

Or, 2x > 8

⇒ x > 4

Hence, we get,

For x > 4, f (x) > g (x)