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

1.	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)?
Answer» 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)

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)?

Answer»

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)