Question

What is the range of the function f(x) = √(x-8) + 6 when f(x) > -8 ?

a) x > -2
b) x > -6
c) x > 6
d) x > 8

Answer 1

The range of the function f(x) = √(x-8) + 6 when f(x) > -8 is x > 204.

Step-by-step explanation:

The range of a function represents the set of all possible output values. To find the range of the function f(x) = √(x-8) + 6 when f(x) > -8, we need to determine the set of values that satisfy this condition.

First, let's set up the inequality:

f(x) > -8

√(x-8) + 6 > -8

Next, we'll isolate the square root term:

√(x-8) > -14

Now we square both sides of the inequality:

x - 8 > 196

x > 204

Therefore, the range of the function f(x) = √(x-8) + 6 when f(x) > -8 is x > 204.