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.
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)` .
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.