Find the domain and range of the following functions interval notation $f(x)=x^2+4x$ and $g(x)=6/(1-x)$ ?

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Answer 1 · 2017-02-02T11:43:45

$(1):f: RR to [-4,oo).$

$(2):g: (-oo,1)uu(1,oo) to (-oo,0)uu(0,oo).$

We will discuss the Soln. in $RR.$

$f(x)=x^2+4x.$

So, to operate $f$ , we can take choose any $x$ from $RR$ ,

meaning that, the Domain is $RR$ .

Next, we note that, $f(x)=x^2+4x=(x^2+4x+4)-4=(x+2)^2-4.$

Also, $AA x in RR, (x+2)^2>=0;" adding "-4, (x+2)^2-4>=-4.$

$rArr f(x)>=-4$

$:." The Range is "[-4, oo).$

Regarding, $g(x)=6/(1-x)," we can not divide by 0; so, "(1-x)ne0.$

In other words, the Domain of

$g" is "RR-{1}=(-oo,1)uu(1,oo)$ .

Further, since, $g(x)=6(1/(1-x)), and, AA x in RR-{1}, 1/(1-x)ne0$

$rArr g(x)ne0.$

$rArr " the Range of g is "RR-{0}=(-oo,0)uu(0,oo).$

Enjoy Maths.!

Find the domain and range of the following functions interval notation f(x)=x^2+4xf(x)=x^2+4x and g(x)=6/(1-x)g(x)=6/(1-x) ?