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2 years ago

Let f(x)=2x-1 and g(x)=1/x. Find the value of f(g(7))

Mathematics

1 answer:

netineya [11]2 years ago

3 0

Answer:

-5/7

Step-by-step explanation:

We need to find g(7) first

All we have to is plug 7 in the place of x

g(7) = 1/7

Now we have f(1/7) = 2x - 1

f(1/7) = 2(1/7) - 1

f(1/7) = 2/7 - 1

Don't forget about common denominators

2/7 - 7/7 = -5/7

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katovenus [111]

Answer:

Step-by-step explanation:

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2 years ago

How can a sequence of transformations be used to justify whether two figures are congruent or similar?

Lena [83]

Answer:

A sequence of transformation can move two congruent figures to the same place (vertical / horizontal shifts). This causes them to perfectly overlap, proving their congruency.

A sequence of transformations can be used to show that something is similar, because if one were to transform a figure with only shrinks / stretches, one can shrink / stretch them to make them congruent. If only shrinks or stretches were done, and if the result of the transformation is congruent to the other figure, then the figures are similar (sides are proportional and shrinking/stretching them proves proportionality to other figure).

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2 years ago

Translate the sentence into an equation.

nekit [7.7K]

Answer:

6c - 7 = 5

Step-by-step explanation:

following the steps in the sentence.

because it is 7 less you have a subtraction problem ( -7)

because it is 6 and a number you have a multiplication problem (6c)

it equals 5 (=5)

8 0

2 years ago

angelo's mother put $50 on a lunch card he spends the same amount each day for lunch. what is the constant rate of change for th

Rina8888 [55]

Given that Angelo spends the same amount everyday from the amount in

the lunch card, the function of the amount remaining is a linear function.

The constant rate of change of the function is; -5.25

The two ordered pair used to find the constant rate of change are; (1, 44.75) and (2, 39.5)

Reasons:

The amount Angelo's mother put on the lunch card = $50

A possible table of values to the question is presented as follows;

$\begin{tabular}{r|c|c|c|c|}Days&0&1&2&3\\Money Remaining&&44.75&39.5&\end{array}\right]$

Required:

The constant rate of the function that gives the amount remaining from the

amount Angelo's mother put on his lunch card.

Solution:

$Slope \ or \ constant \ rate \ of \ change = \mathbf{\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}}$

The two ordered pair that can be used to find the slope or constant rate of change are;

(x₁, y₁) = (1, 44.75), and (x₂, y₂) = (2, 39.5)

With the above two ordered pairs, we have the constant rate of change of the function given as follows;

$Constant \ rate \ of \ change\ (The \ slope) =\dfrac{39.5-44.75}{2-1} = \mathbf{ -5.25}$

The constant rate of change for the function that gives the amount remaining in the lunch card is; -5.25

Learn more about the constant rate of change of a function here:

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3 0

2 years ago

Find a polynomial of degree 3 with real coefficients and zeros of -3,-1, and 4, for which f(-2)=-24

Zanzabum

We want to find a polynomial

f(x) = a x³ + b x² + c x + d

such that the roots of f are x = -3, x = -1, and x = 4, and f(x) takes on a value of -24 when x = -2.

The factor theorem for polynomials tells us that we can factorize f(x) as

a x³ + b x² + c x + d = a (x + 3) (x + 1) (x - 4)

Expand the right side:

(x + 3) (x + 1) (x - 4) = x³ - 13x - 12

So we have

a x³ + b x² + c x + d = a x³ - 13a x - 12a

In order for both sides to be equal, the coefficients of both polynomials on terms of the same degree must be equal. This means

a = a (of course)

b = 0 (there is no x² term on the right)

c = -13a

d = -12a

We also have that f (-2) = -24, which means

f (-2) = a (-2 + 3) (-2 + 1) (-2 - 4)

-24 = 6a

a = -4

which in turn tells us that c = 52 and d = 48.

So we found

f(x) = -4x³ + 52x + 48

4 0

2 years ago