Which of the following functions has its domain identical...

Transcript

00:01 In this question, we are given four functions, and we are asked to determine for which of these four functions, the domain of the function is the same as the range of the function.

00:10 To do that, we need to recall the graph of each function.

00:14 So the first function is f of x is equal to x squared.

00:22 That's a standard parabola.

00:27 And recall that the graph of the standard parabola looks like this.

00:35 So basically, it's defined for all values of x.

00:41 The domain of the parabola is negative infinity to positive infinity.

00:46 But look at the range.

00:47 Whatever number you plug in in this function, it's always going to be a positive number, right? so therefore, the range of this function is going to be from zero to infinity.

01:02 And you can see that they are not equal.

01:06 So for a domain is not equal to the range.

01:11 Let's move on to the next one.

01:14 G of x is equal to square root of x.

01:22 Here is the graph of the function.

01:25 Recall that it's a parabola which opens along the x -axis, and it doesn't have a branch in the fourth quadrant.

01:40 So let's look at the domain of this function.

01:43 Since it's a square root function, it cannot take negative numbers as arguments.

01:49 So the domain is going to be from zero to infinity.

01:51 It can be either zero or a positive number.

01:57 Now the range, since it's a square root and the values of square root are always positive, the range is also going to be from zero to infinity...

Question

Which of the following functions has its domain identical with its range? (a) $ f(x)=x^{2}$ (b) $g(x)=\sqrt{x}$ (c) $h(x)=x^{3}$ (d) $i(x)=|x|$

Question

Which of the following functions has its domain identical with its range? (a) $ f(x)=x^{2}$ (b) $g(x)=\sqrt{x}$ (c) $h(x)=x^{3}$ (d) $i(x)=|x|$

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