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2 years ago

If f(x)=1/2 x-6 what is the equation for f–1(x)?

Mathematics

2 answers:

Tomtit [17]2 years ago

6 0

Answer:

Option C $f^{-1}(x)=2(x+6)$

Step-by-step explanation:

we have that

$f(x)=\frac{1}{2}x-6$

Let

$y=f(x)$

$y=\frac{1}{2}x-6$

Exchange the variables x for y and y for x

$x=\frac{1}{2}y-6$

Isolate the variable y

$x+6=\frac{1}{2}y$

$y=2(x+6)$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=2(x+6)$

Mumz [18]2 years ago

5 0

I hope this helps you

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A farmer has 20 acres to plant in wheat and barley. He has to plant at least 15 acres. Wheat costs $200 per acre to plant and ba

maria [59]

Answer:

16 acres of barley only (no acres of wheat)

Step-by-step explanation:

A graph shows cost of planting puts an upper limit on planted area. The lower limit is provided by the requirement to plant at least 15 acres. The vertices of the feasible solution region are ...

(wheat acres, barley acres) = {(0, 15), (0, 16), (3, 12)}

The profit associated with these scenarios will be ...

for (0, 16): 16·350 = 5600

for (3, 12): 3·450 +12·350 = 1350 +4200 = 5550

To maximize profit, the farmer should plant 16 acres of barley.

4 0

3 years ago

Simplify 7x+42/x^2+13x+42

o-na [289]

2(10x^3+21x^2+21
x^2

5 0

2 years ago

Fabio and Gwen are saving money to buy a new gaming station. They need at least $510 to purchase the new gaming station. Gwen we

vaieri [72.5K]

x represents the number of lawns weeded by Gwen and y represents the number of dogs walked by Fabio.

Gwen charges $12 each time she weeds a yard and Fabio charges $9 each time he walks a dog.

So, for x number of weeds, Gwen earned 12x and for y number of dogs walked, Fabio earned 9y.

They need at least $510 to purchase the new gaming station.

Therefore,

12x + 9y ≥ 510

Also, the number of dog walks that Fabio has scheduled should not be more than twice the number of yards Gwen has scheduled to weed.

Therefore,

y ≤ 2x

Also, Fabio will walk at least 25 dogs.

Therefore,

y ≥ 25

Hence, the constraints are:

12x + 9y ≥ 510

y ≤ 2x

y ≥ 25

8 0

3 years ago

One night Puvi spent 1/3 of his money on dinner and then 1/4 of the remaining money on dessert. He then had just enough left so

arsen [322]

Answer:

Step-by-step explanation:

Cost of two tickets = 2 * 30 = £60

Let the amount with Puvi = £x

Money spent on dinner = (1/3)*x

$= \dfrac{1}{3}x$

$Remaining \ money =x - \dfrac{1}{3}x =\dfrac{3}{3}x-\dfrac{1}{3}x=\dfrac{2}{3}x$

$Money \ spent \ on \ dessert = \dfrac{1}{4} *\dfrac{2}{3}x =\dfrac{1}{6}x\\\\\\$

Total money - money spent on dinner - money spent on dessert = 60

$x -\dfrac{1}{3}x -\dfrac{1}{6}x=60\\\\\\\dfrac{6}{6}x-\dfrac{1*2}{3*2}-\dfrac{1}{6}x =60\\\\\\\dfrac{6}{6}x-\dfrac{2}{6}x-\dfrac{1}{6}x=60\\\\\\\dfrac{6-2-1}{12}x=60\\\\\\\dfrac{3}{12}x=60\\\\\\x=60*\dfrac{12}{3}=60*4=240$

Money that Puvi had at the start of the night = £ 240

8 0

2 years ago

Given f(x) = 5x + 7,g(x) = 3x-1 find f(g(x))

kakasveta [241]

Answer:

f(g(x)) = 15x + 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Distributive Property

Algebra I

Functions
Function Notation
Composite Functions

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 5x + 7

g(x) = 3x - 1

Step 2: Find

Substitute in functions: f(g(x)) = 5(3x - 1) + 7
[Distributive Property] Distribute 5: f(g(x)) = 15x - 5 + 7
[Addition] Combine like terms: f(g(x)) = 15x + 2

7 0

2 years ago