Question

3. Consider the function below and figure out the intervals for its domain, and write it in the formats requested. f(x) = Vx+4 x-1 a) shade the domain on the number line b) write in interval notation: c). write in inequality notation:

Answer 1

3 f (x) = Joct4 X-1 a ) -6-5-4-3-2-1 0 1 2 3 4 5 6 6 ) f Combining Find non negative values for radical x3,-4 function is undefined at x = 1 these two -4<x< 1 or x>! Interval notation : [-4,DU(1,0) c) Inequality notation -4<x<I or oc>l

Answer 2

SOLUTION :

f(x) = sqrt(x + 4) / (x - 1)

So, x ≠ 1 and x ≥ - 4 (to ensure that  sqrt is of a positive value or 0)

Hence,  1 > x > 1 and x ≥ - 4 

a. Number line for domain :

  << ————@===========o==========>>

  - ∞              - 4                       1                      ∞

b.

Interval notation :

Domain : [ - 4,  1) U (1, ∞)   (ANSWER)

c.

Inequality notation :

x ≠ 1 and x ≥ - 4 (ANSWER).