Question

What are the domain and range of the function? f(x)=3√x−1 ?

A) Domain: (−∞, ∞)

Range: (−∞, ∞)

B) Domain: [0, ∞)

Range: [1, ∞)

C) Domain: ​​ [1, ∞)

Range: ​ (−∞, ∞) ​

D) Domain: [1, ∞)

Range: [0, ∞)

Answer 1

Find the domain by finding where the function is defined. The range is the set of valves that correspond with the domain.

Domain; (0, infinity) , {x/x > 0)

for any integer

Range; (-1, infinity) , {y/y > -1)

Answer 2

The domain and the range of a graph is the possible x and y values, the graph can take.

• The domain of the function is: $[1,\infty)$
• The range of the function is: $[0,\infty)$

Given that:

$f(x) = 3\sqrt{x-1}$

Set the radicand to 0

$x - 1 = 0$

Solve for x

$x = 1+0$

$x= 1$

This means that for the function to have a real value, the value of x must be 1 or more.

So, the domain is: $[1,\infty)$

When $x = 1$

$f(x) = 3 \times \sqrt{1-1}$

$f(x) = 3 \times \sqrt{0}$

$f(x) = 3 \times 0$

$f(x) = 0$ --- this represents the minimum y value.

So, the range is: $[0,\infty)$

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