Find the domain and range of f(x) = 2 square root of x-2

1 answer:

5 0

$f(x)=2\sqrt{x-2}\\\\The\ domain:\\x-2\geq0\to x\geq2\\\boxed{x\in[2;\ \infty)}\\\\The\ range:\\\boxed{y\in[0;\ \infty)}$

$If\ f(x)=2\sqrt{x}-2,\ then\\\\The\ domain:\boxed{x\in[0;\ \infty)}\\\\The\ range:\boxed{y\in[-2;\ \infty)}$

You might be interested in

Long division<br> 3x+1/6x^6+5x^5+2x^4-9x^3+7x^2-10x+2

inna [77]

$(6 x^{6}+5x^{5}+2x^{4}-9x^{3}+7x^{2}-10x+2) / (3x+1)$

We divide first number from first parenthesis with first number from second parenthesis. Then the resulting number we multiply by all numbers in second parenthesis and substract from first parenthesis.

$6 x^{6}/3x = 2 x^{5} \\ \\ 6 x^{6}+5x^{5}+2x^{4}-9x^{3}+7x^{2}-10x+2 - 6 x^{6} -2 x^{5} = 3x^{5}+2x^{4}-9x^{3}+7x^{2}-10x+2\\$

We repeat previous steps until we run out of numbers:
$3x^{5}/3x=x^{4} \\ \\ 3x^{5}+2x^{4}-9x^{3}+7x^{2}-10x+2-3x^{5}-x^{4}= \\ \\ x^{4}-9x^{3}+7x^{2}-10x+2 \\ \\ \\ x^{4}/3x= \frac{1}{3} x^{3} \\ \\ x^{4}-9x^{3}+7x^{2}-10x+2-x^{4}- \frac{1}{3} x^{3}= \\ \\ - \frac{28}{3} x^{3}+7x^{2}-10x+2 \\ \\ \\ - \frac{28}{3} x^{3}/3x= - \frac{28}{9} x^{2} \\ \\ - \frac{28}{3} x^{3}+7x^{2}-10x+2+ \frac{28}{3} x^{3}+ \frac{28}{9} x^{2} = \\ \\ \frac{91}{9} x^{2}-10x+2$
$\frac{91}{9} x^{2}/3x=\frac{91}{27} x \\ \\ \frac{91}{9} x^{2}-10x+2-\frac{91}{9} x^{2}-\frac{91}{27} x= \\ \\ -\frac{361}{27} x+2 \\ \\ \\ -\frac{361}{27} x/3x=-\frac{361}{81} \\ \\ -\frac{361}{27} x+2+\frac{361}{27}x+\frac{361}{27}= \\ \\ \frac{415}{27}$

We are left with a number that has no x inside. This is remainder.
The final solution is sum of all these solutions and remainder:
$(2 x^{5}+x^{4}+\frac{1}{3} x^{3} - \frac{28}{9} x^{2} +\frac{91}{27} x)+(-\frac{361}{81} )$

6 0

3 years ago

27% of £396.58<br> Give your answer rounded to 2 DP.

shusha [124]

Answer:

£107.08

Step-by-step explanation:

percentage multiplier is 0.27

396.58 x 0.27 = 107.0766

to 2dp = £107.08

3 0

3 years ago

Please help me!!!!!!!!!!!!

insens350 [35]

How I can’t bring them to you

3 0

3 years ago

Joe gave the following argument: Since lim x→0 0 = 0,

lions [1.4K]

No error - A and B are completely right, and using the subtraction law D is right

7 0

3 years ago

Use front end estimation with adjustment to estimate each difference..5780-3962

inessss [21]

Idk what to do on yalls problems

4 0

3 years ago