D(f)=(3,9)
R(f)=[4,6]
I got Domain = (3,9) and Range= [9,13]. Am i on the right track?
If this is true could you please explain to me why the Domain doesn't change between the two functions.
Thankyou!
R(f)=[4,6]
I got Domain = (3,9) and Range= [9,13]. Am i on the right track?
If this is true could you please explain to me why the Domain doesn't change between the two functions.
Thankyou!
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You have the right answers. The domain does not change just because modifications (such as multiplying by 2, or adding 1) are made after an element of the domain has been used to find the function's value.
2f(x)+1 is the equivalent of g(f(x)), where g(x) = 2x + 1. g(x) operates on whatever value is produced by f(x) when f(x) is applied to a number in its domain.
2f(x)+1 is the equivalent of g(f(x)), where g(x) = 2x + 1. g(x) operates on whatever value is produced by f(x) when f(x) is applied to a number in its domain.
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You are correct.
Domain does not change as the entire expression 2f(x) + 1 is defined for the original values. If you're comfortable with composite functions, you can think of this as g[f(x)] where g(x) = 2x + 1.
Suppose the expression looked like this instead:
f(x) / (x - 4)
In this case, the domain would exclude 4 as the expression is undefined when x = 4.
Domain does not change as the entire expression 2f(x) + 1 is defined for the original values. If you're comfortable with composite functions, you can think of this as g[f(x)] where g(x) = 2x + 1.
Suppose the expression looked like this instead:
f(x) / (x - 4)
In this case, the domain would exclude 4 as the expression is undefined when x = 4.