The domain of the function f(x) = √(x +c) -3, is [-c , ∞) where -c in included in domain .
What is the domain of the function ?
The domain of a function is the set of all possible inputs for the function.
In other words, the domain of f(x) is the set of all those real numbers for which f(x) is meaningful.
For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.
Step 1:
Put y = f(x)
Step 2:
Solve the equation y = f(x) for x in terms of y.
Step 3 :
Find the values of y for which the values of x, obtained from x = g(y) are real and its domain of f.
So, to find domain for given function :
y = √(x +c) -3
y+3 = √x +c
(y+3)² = x +c
(y+3)² - c = x
So, the least value of x is -c when (y+3) become zero at y = -3.
And for any value of y , (y+3)² will always be positive.
So x ∈ [-c,∞) i.e. domain of function.
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