Question

For the questions below, enter your answers using interval notation. You can use "U" to represent a "union", e.g. enter "(1,2) U (3,5)" for ( 1 , 2 ) ∪ ( 3 , 5 ) . You can enter "oo" for ∞ , e.g. enter "(-oo, oo)" for ( − ∞ , ∞ ) .
Suppose f(x)=2x2+4 What is the domain of f What is the range of f?

Suppose g(x)=√x−3/x−8 What is the domain of g? What is the range of g?

Answer 1

1) Given that

$f(x) = 2x^2+4$

We find that this is a parabola with vertex at (0.4) open up.

x can take any real value.

So domain of f = (-∞,∞)

Since open up with vertex at (0,4) y cannot take values <4

Range = [4,∞)

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2) $g(x) = x^{1/2} -\frac{3}{x} -8$

Because x is in denominator x cannot equal 0

Also first term is square root of x.  Hence x can be only positive

So domain is [0,∞)

When x increases y also increases indefinitely.

Hence range = (-∞,∞)