Question

Okay so I need help with basically how to find the domain, range, and how to solve if it says Find the value of f(3).

Let the f function be defined by f(x) = the square root of x + 1 for -1 is less than or equal to x less than or equal to 3.
And 4 - x for 3 is less than x less than or equal to 5

I don't know where to start. Thanks in advance.

Answer 1

we have:

f(x) =
{√(x+1) for -1 <= x <= 3
{4-x for 3 < x <= 5

domain:
square root is only defined for positive values. So, we need x+1 >= 0, or x >= -1. 4-x is defined for all real x.
So, domain is [-1,5]

range:
for -1 <= x <= 3, 0 <= f(x) <= 2
for 3 < x <= 5, -1 <= f(x) < 1
so, the range is [-1,2]

f(3) = √(3+1) = √4 = 2