Question:
Let 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)?
(b) For what real numbers x, f (x) < g (x)?
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)