- #1

chwala

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- Homework Statement
- The real functions ##f## and ##g## are given by

##f(x)=x-3## and ##g(x)=\sqrt {x}##

Find the domain and the range of ##f-3g##

- Relevant Equations
- Functions

Am refreshing on this,

For the domain my approach is as follows,

##(f-3g)x = f(x)-3g(x)##

##=x-3-3\sqrt{x}##.

The domain of ##f-3g## is given by ##f∩g = [{x: x ≥0}]##

We have

##y= x-3-3\sqrt{x}=(\sqrt x-\frac{3}{2})^2-\dfrac{21}{4}##.

The least value is given by; ##\left(\sqrt x-\dfrac{3}{2}\right)^2 =0##. This occurs when ##x=2.25##.

The range of ##f-3g## is the set ##[{y: y≥-5.25}]##

Your insight or correction is welcome.

For the domain my approach is as follows,

##(f-3g)x = f(x)-3g(x)##

##=x-3-3\sqrt{x}##.

The domain of ##f-3g## is given by ##f∩g = [{x: x ≥0}]##

We have

##y= x-3-3\sqrt{x}=(\sqrt x-\frac{3}{2})^2-\dfrac{21}{4}##.

The least value is given by; ##\left(\sqrt x-\dfrac{3}{2}\right)^2 =0##. This occurs when ##x=2.25##.

The range of ##f-3g## is the set ##[{y: y≥-5.25}]##

Your insight or correction is welcome.

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