Question

2
If f(x)= x2 + 5x + 7, then the value of x for which f(x) = f(x+1) is
(a) 3
(b) - 6
(C) -3
(d) 6​

Answer 1

Answer:

If f(x)= x2 + 5x + 7, then the value of x for which f(x) = f(x+1) is

(a) 3

(b) - 6

(C) -3

(d) 6

Answer 2

Given: f(x) = x² + 5x + 7

To find: The value for x for which f(x) = f(x+1)

Solution: According to the question, we need to check if

f(x) = f(x+1)

⇒ x² + 5x + 7 = (x+1)² + 5(x+1) + 7

⇒ x² + 5x = x² + 2x + 1 + 5x + 5

⇒ 0 = 2x + 6

⇒ 2x = -6

⇒ x = -3

Therefore, the value of x for which f(x) = f(x+1) is -3.

Answer: Option (C) -3