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givi [52]
2 years ago
11

Given that f(x) = x2 – 3x - 10 and g(x) = x – 5, find (f - g)(x) and express

Mathematics
2 answers:
Roman55 [17]2 years ago
8 0

Answer:

(f-g)(x)= x^2-4x-5

Step-by-step explanation:

We have the two functions:

f(x)=x^2-3x-10\text{ and } g(x)=x-5

And we want to find (f-g)(x).

(f-g)(x) is equivalent to f(x)-g(x).

Therefore:

\begin{aligned} (f-g)(x)&=f(x)-g(x)\\ &=(x^2-3x-10)-(x-5)\end{aligned}

Simplify:

\begin{aligned} &=x^2-3x-10-x+5 \\ &=(x^2)+(-3x-x)+(-10+5) \\ &=x^2-4x-5\end{aligned}

Therefore:

(f-g)(x)= x^2-4x-5

Nookie1986 [14]2 years ago
7 0

Answer:

x^2 -3x+5 = 0

Step-by-step explanation:

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Notation

The inverse of the function f is denoted by f -1 (if your browser doesn't support superscripts, that is looks like f with an exponent of -1) and is pronounced "f inverse". Although the inverse of a function looks like you're raising the function to the -1 power, it isn't. The inverse of a function does not mean the reciprocal of a function.

Inverses

A function normally tells you what y is if you know what x is. The inverse of a function will tell you what x had to be to get that value of y.

A function f -1 is the inverse of f if

<span><span>for every x in the domain of f, f<span> -1</span>[f(x)] = x, and</span><span>for every x in the domain of f<span> -1</span>, f[f<span> -1</span>(x)] = x</span></span>

The domain of f is the range of f -1 and the range of f is the domain of f<span> -1</span>.

Graph of the Inverse Function

The inverse of a function differs from the function in that all the x-coordinates and y-coordinates have been switched. That is, if (4,6) is a point on the graph of the function, then (6,4) is a point on the graph of the inverse function.

Points on the identity function (y=x) will remain on the identity function when switched. All other points will have their coordinates switched and move locations.

The graph of a function and its inverse are mirror images of each other. They are reflected about the identity function y=x.

6 0
3 years ago
Lauren bikes 1 1/3 miles in 1/1/0 hour. What is her rate of speed in miles per hour?
Amanda [17]

speed = distance / time

1 1/3 = 4/3

so

speed = (4/3) / (1/10)

= (4/3) * 10

= 40/3 mph

or 13 1/3 mph

Hope this helps!

3 0
3 years ago
Write a set of three numbers that have a GCF of 13.
vitfil [10]
Right now, I can only think 26 and 39.
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3 years ago
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The price of a book is $45 the sale tax is 4.5% what is the total price of the book​
Murljashka [212]

Answer:

About 47.03 dollars

Step-by-step explanation:

4.5 percent of 45 is 2.025.

Add that to original price of 45.

Round to the nearest tenth.

Hope this helps!

8 0
3 years ago
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Drag the tiles to the boxes to form correct pairs. Polygon ABCD is defined by the points A(-4, 2), B(-2, 4), C(1, 3), and D(2, 2
Ber [7]

Answer:

D'(-2, 2); C''(3, -1); A'''(4, -2); and B''(4, 2)

Step-by-step explanation:

For D', we rotate the point (2, 2) 90° counterclockwise. This maps every point (x, y)→(-y, x); it takes (2, 2)→(-2, 2).

For C'', we rotate the point (1, 3) 90° clockwise.  This maps every point (x, y)→(y, -x); it takes (1, 3)→(3, -1).

For A''', we rotate the point (-4, 2) 180° clockwise.  This maps every point (x, y)→(-x, -y); it takes (-4, 2)→(4, -2).

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7 0
3 years ago
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