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sergey [27]
3 years ago
15

What is the inverse of the function f(x) = 2x + 1?

Mathematics
1 answer:
Alexandra [31]3 years ago
6 0

Answer:

f^{-1}(x) = \frac{x-1}{2}

Step-by-step explanation:

let y = f(x) and rearrange making x the subject, that is

y = 2x + 1 ( subtract 1 from both sides )

y - 1 = 2 ( divide both sides by 2 )

\frac{y-1}{2} = x

Change y back into terms of x and let x = f^{-1} (x), thus

f^{-1}(x ) = \frac{x-1}{2}

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Taletha is preparing for an exam in Algebra II. She knows she will be expected to determine if two functions are inverses of eac
seropon [69]

Answer:

f ○ g(x) = x and g ○ f(x) = x  is the correct composition

Step-by-step explanation:

INVERSE FUNCTIONS: Two functions are said to be inverse of each other if for every y = f(x), there exists a function g(x),

such that x = f^{-1} (y) =  g(y)

Now, here if we need to show tha two functions f(x) and g(x) are inverse functions of each other , then show that for every x:

1. f  o g(x)   =   f(g(x))= x

2. g o f(x)  =  g(f(x))   = x

If any two functions satisfy these two conditions, then they are inverse of each other.

5 0
4 years ago
What is the eighth term in the arithmetic sequence defined by the explicit formula
RideAnS [48]

Answer:

Find out the what is the eighth term in the arithmetic sequence defined by the explicit formula.

a_{n} = 2n + 7

To prove

As given the explicit formula for the arithmetic sequence .

a_{n} = 2n + 7

Put n = 8

a_{8} = 2\times 8 + 7

a_{8} = 16 + 7

a_{8} = 23

Therefore the eighth term in the arithmetic sequence is 23 .




5 0
3 years ago
Read 2 more answers
Lin lines the bottom of her first pan with aluminum foil. The area of the rectangular piece of foil 11 1 4 is square inches. Its
prisoha [69]

Answer:

Length =

= 5/2 inches or 2 1/2 inches

Step-by-step explanation:

Lin lines the bottom of her first pan with aluminum foil. The area of the rectangular piece of foil 11 1 4 is square inches. Its length is 4 1 2 inches. What is the width of the foil? Explain your reasoning.

Area of rectangle = Length × Width

Widths = Area/Length

The area of the rectangular piece of foil 11 1/4 is square inches.

Its length is 4 1 /2 inches.

Hence:

Length = 11 1/4 /4 1/2

= 45/4 ÷ 9/2

= 45/4 × 2/9

= 5/2 inches

= 2 1/2 inches

6 0
3 years ago
Without calculating, is the equation (1.8 times 3) times 2.1 = ( 1.8 times 2.1 ) true or false? Explain your reasoning.
Paladinen [302]
It is true due to the commutative property of multiplication. If all of your operations are multiplication, then the integers can move around and you can still get the same answer. 
^This is only true if you meant to type (1.8x3)x2.1=(1.8x2.1)x3

If you meant what you typed, then the equation is false. The left side would be 3 times the value of the right side due to the 3 being on the left side and not the right side while without the 3 the two sides would be equal.
6 0
3 years ago
One corner of a rectangle has the ordered pair of (8, 2). The rectangle is dilated by a scale factor of 4. What is the new order
faust18 [17]
The new ordered pair would be 11,6
8 0
3 years ago
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