Question

F(x) = |2x + 1| + 3

g(x) = -2
find (f + g)(x)
A.(f + g)(x) = |2x + 2|
B.(f + g)(x) = |2x| + 2
C.(f + g)(x) = |2x + 1| + 1
D.(f + g)(x) = |2x + 4| - 2

Answer 1

(f + g)(x) = I2x + 1I + 1 ⇒ C

Explanation:

Let us solve the question

∵ f(x) = I2x + 1I + 3

∵ g(x) = -2

→ We need to find (f + g)(x), which means add the two functions

∵ (f + g)(x) = f(x) + g(x)

→ Substitute the right side of each function on the right side

∴ (f + g)(x) = I2x + 1I + 3 + (-2)

→ Remember (+)(-) = (-)

∴ (f + g)(x) = I2x + 1I + 3 - 2

→ Add the like terms in the right side

∵ (f + g)(x) = I2x + 1I + (3 - 2)

∴ (f + g)(x) = I2x + 1I + 1