FUNCTIONS

h(x)= 3^x

a) Solve the equation h^-1(x)= 2

Answers

Answer 1

Answer: Because the inverse of function h(x) = 3^x is h^-1 ( x ) = log 3 ( x ) , we solve the equation log 3 ( x ) = 2 ;
3^2 = x;
x = 9 ;

Answer 2

Answer: Use the property of inverse functions:
$h(h^(-1)(x))=x \n \n\hbox{if} \n h^(-1)(x)=2 \n \hbox{then} \nh(2)=x \n\Downarrow \nh(x)=3^x \nh(2)=3^2 \nh(2)=9 \n \n\boxed{x=9}$

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Jerry buys three jeans at $39.98 each the sales tax on clothes is a punch to 5% what is the total cost of the sale?

Answers

Answer: $43.28

Step-by-step explanation: To find the sales tax, first convert 8.25% to a decimal. 8.25% as a decimal is 0.0825.

Now simply multiply 0.0825 x 39.98 which equals about 3.30

So, the total sales tax is $3.30

Now add $3.30 to $39.98 which equals a total cost of $43.28

(12.8)2 - (30+0.375)

Answers

Answer:

-4.775

Step-by-step explanation:

What is the name of the shape of the graph of a quadratic function? A. hyperbola B. parabola C. line D. quadratic

Answers

we are given

graph of a quadratic function

Quadratic function:

Those function which has degree=2

we can write it as

$y=ax^2+bx+c$

Since, the degree is 2

so, the shape of the curve will be parabolic

so, option-B.........Answer

If G = {(-1, 7),(-8, 2),(0, 0),(6, 6)}, then the range of G is

Answers

Answer with explanation:

All the first element of Ordered pair ,is called Domain of the set. And all the second element of Ordered pair is called Range.

For, the ordered pair, (x,y)

x= Domain

y=Range

For, the Set G ,Consisting of ordered pair

= {(-1, 7),(-8, 2),(0, 0),(6, 6)}

⇒Domain of G = {-1, -8, 0,6}

⇒Range of G= {2, 7, 0, 6}

All the second numbers. {0, 2, 6, 7}.

What is the difference of the polynomials?

(–2x3y2 + 4x2y3 – 3xy4) – (6x4y – 5x2y3 – y5)

Answers

Answer:

$-6x^4-2x^3y^2+9x^2y^3-3xy^4+y^5$

Step-by-step explanation:

We have to find the difference of the polynomials

$(-2x^3y^2+4x^2y^3-3xy^4)-(6x^4-5x^2y^3-y^5)$

Let us distribute the negative over the parenthesis

$-2x^3y^2+4x^2y^3-3xy^4-6x^4+5x^2y^3+y^5$

Now, group the like terms

$-2x^3y^2+(4x^2y^3+5x^2y^3)-3xy^4-6x^4+y^5$

Combine the like terms

$-2x^3y^2+9x^2y^3-3xy^4-6x^4+y^5$

Rearrange the polynomial, we get

$-6x^4-2x^3y^2+9x^2y^3-3xy^4+y^5$

Answer
9x^2 y^3-2x^3 y^2-3xy^4-6x^4 y+y^5

Explanation
The term difference in mathematics means the result after subtraction.
It is important to know that we only subtract like terms only.
(-2x^3 y^2+4x^2 y^3-3xy^4 )-(6x^4 y-5x^2 y^3-y^5)
(-2x^3 y^2+4x^2 y^3-3xy^4 )-6x^4 y+5x^2 y^3+y^5
-2x^3 y^2+4x^2 y^3-3xy^4-6x^4 y+5x^2 y^3+y^5
-2x^3 y^2+9x^2 y^3-3xy^4-6x^4 y+y^5
This equation cannot be simplified further. So the difference is
=9x^2 y^3-2x^3 y^2-3xy^4-6x^4 y+y^5

Use summation notation to write the series2+4+6+8+... For 10 terms