Find the domain and range of the following functions; a) f(x) = 2x-3  g(x)= 3x+1 b) f(x) = `sqrt(x-4)`  g(x) = x+2 I'm confused on how I am supposed to get the domain and range for these...

Find the domain and range of the following functions;

a) f(x) = 2x-3  g(x)= 3x+1

b) f(x) = `sqrt(x-4)`  g(x) = x+2

I'm confused on how I am supposed to get the domain and range for these functions. 

Asked on by bluro

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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Domain and range represent all the `x` values and all the `y` values for the given function. With straight line (linear) functions, the domain and range ordinarily extend between infinity and negative infinity.

a) `f(x) = 2x- 3` As there are no restrictions or points given, the domain and range will be:

`x in(- oo; oo)`  (domain) and `y in(-oo; oo)` (range). 

`g(x) = 3x+1 therefore x in (-oo; oo) ` and `y in( -oo; oo)`

b) `f(x) = sqrt(x-4)` We cannot have a negative value inside the square root  and therefore we will solve when `x-4gt0`

 The domain is represented as `gt=` . The range can be identified most easily through the use of a graph. We know that we are only working with the positive `sqrt(x-4)` as the question does not require `- sqrt(x-4)`

The graph will be as follows: 

 

The range will be `ygt=0` .

`g(x) = x+2` . therefore `x in (-oo; oo)` and `y in(-oo; oo)` .

Ans:

Therefore, it can be seen that for straight line (linear) functions, domain and range can be represented as: 

`x in (-oo; oo); y in (-oo;oo)`

and for radical functions (with a square root), work from inside the root.  

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