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1 year ago

G(3)=g, left parenthesis, 3, right parenthesis, equals

1 answer:

6 0

The inverse function will be g(x) = (x + 3) / 5. Then the value of the function f(5) and g(3) will be 22 and 6/5.

<h3>What is inverse of a function?</h3>

Let the function will be

f: X → Y

Then the inverse function will be

f⁻¹: Y → X

The function is given below.

f(x) = 5x – 3

Then the value of the function f(x) at x = 5, will be

f(5) = 5 × 5 – 3

f(5) = 22

The g(x) is the inverse function of f(x).

Then the function g(x) will be

5g(x) – 3 = x

g(x) = (x + 3) / 5

Then the value of function g(x) at x = 3, will be

g(3) = (3 + 3) / 5

g(3) = 6 / 5

The complete question is given below.

The function f(x) = 5x – 3. And the function g(x) is the inverse of f(x). Find the value of the function f(5) and g(3).

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3. Classify each function according to whether it is a vertical stretch, a vertical compression, a horizontal

Vladimir79 [104]

The classifications of the functions are

A vertical stretch --- p(x) = 4f(x)
A vertical compression --- g(x) = 0.65f(x)
A horizontal stretch --- k(x) = f(0.5x)
A horizontal compression --- h(x) = f(14x)

<h3>How to classify each function accordingly?</h3>

The categories of the functions are given as

A vertical stretch
A vertical compression
A horizontal stretch
A horizontal compression

The general rules of the above definitions are:

A vertical stretch --- g(x) = a f(x) if |a| > 1
A vertical compression --- g(x) = a f(x) if 0 < |a| < 1
A horizontal stretch --- g(x) = f(bx) if 0 < |b| < 1
A horizontal compression --- g(x) = f(bx) if |b| > 1

Using the above rules and highlights, we have the classifications of the functions to be

A vertical stretch --- p(x) = 4f(x)
A vertical compression --- g(x) = 0.65f(x)
A horizontal stretch --- k(x) = f(0.5x)
A horizontal compression --- h(x) = f(14x)

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4 0

1 year ago

The graph of f ′ (x), the derivative of f of x, is continuous for all x and consists of five line segments as shown below. Given

Rom4ik [11]

$f'(x)\ge0$ for all $x$ in [-3, 0], so $f(x)$ is non-decreasing over this interval, and in particular we know right away that its minimum value must occur at $x=-3$ .

From the plot, it's clear that on [-3, 0] we have $f'(x)=-x$ . So

$f(x)=\displaystyle\int(-x)\,\mathrm dx=-\dfrac{x^2}2+C$

for some constant $C$ . Given that $f(0)=7$ , we find that

$7=-\dfrac{0^2}2+C\implies C=7$

so that on [-3, 0] we have

$f(x)=-\dfrac{x^2}2+7$

and

$f(-3)=\dfrac52=2.5$

5 0

3 years ago

Due to inflation there were two demand increases. After the second increase the price for a certain item became twice as big as

slamgirl [31]

Consider, pls, this option:
1) let start price is 'x' and the 1-t increasing is 'y';
2) after the 1-t increasing new1_price is x(y+1);
3) after the 2-d increasing new2_price is 1.25x(y+1);
4) from another side, new2_price is '2x';
5) according to five items it is possible to make up an equation: 1.25x(y+1)=2x;
1.25(y+1)=2, y=8/5 -1=3/5=0.6.
0.6 means 60%.
Answer: 60%.

4 0

3 years ago

A line has a slope of 1/4 and passes through point (0.4,-1/2). What is the value of the y-intercept?

AVprozaik [17]

Answer: The value of the y-intercept is $-\frac{3}{5}$

Step-by-step explanation:

The equation of the line in Slope-intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

In this case we know that the line passes through point $(0.4,-\frac{1}{2})$ and has a slope of $\frac{1}{4}$ . Then we can substitute the following values into $y=mx+b$ :