Algebra 2
posted by Kendra on .
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.

we have:
f(x) =
{√(x+1) for 1 <= x <= 3
{4x for 3 < x <= 5
domain:
square root is only defined for positive values. So, we need x+1 >= 0, or x >= 1. 4x 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