Given f(x)= x+1 and g(x)=√x+2 determine the following. Write each answer using interval notation.
Determine the Domain of g(f(x))
Domain:

g(f(x)) =

Domain = [-1,∞)

Step-by-step explanation:

Given f(x) = x+1 and g(x) = √x + 2

g(f(x)) is a composite function.

g(f(x)) =

To find the domain of composite function we must get both domains right (the composed function and the first function used).

The domain of f(x) is all the real numbers.

The domain of g(f(x)) is the values of x provide that the square root is greater than or equal zero

So, x+1 ≥ 0

∴ x ≥ -1

So, the domain = [-1,∞)

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)