Question

Let f be the function given by f(x) = x + √(x+1). Find and simplify f(a + 1).

A) a + √a + 1
B) a + 2
C) a + 1 + √(a + 1)
D) a + √(a + 2)

Answer 1

To simplify f(a + 1) = x + √(x+1), substitute (a + 1) for x and simplify to get a + 1 + √(a + 2).

Step-by-step explanation:

To find and simplify f(a + 1) for the function f(x) = x + √(x+1), we substitute (a + 1) for x in the function:

f(a + 1) = (a + 1) + √((a + 1) + 1)

Expanding the expression inside the square root, we get:

f(a + 1) = a + 1 + √(a + 2)

Therefore, the simplified form of f(a + 1) is a + 1 + √(a + 2).