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charle [14.2K]
3 years ago
9

Please help! Please please please

Mathematics
1 answer:
scoray [572]3 years ago
6 0

Answer:

For x ≥ 2, the graph will be a straight line parallel to x-axis and having equation y = - 3

And for x < 2 will be a straight line having equation y = x i.e. the graph makes 45° angle with the positive x-axis and passing through the origin.

Step-by-step explanation:

The piece wise function g(x) is given by  

g(x) = x if x < 2 and g(x) = - 3 if x ≥ 2.

Now, the graph has two parts, one for x ≥ 2 and another for x < 2.

Here, for x ≥ 2, the graph will be a straight line parallel to the x-axis and having equation y = - 3

Again, the graph for x < 2 will be a straight line having equation y = x i.e. the graph makes 45° angle with the positive x-axis and passing through the origin. (Answer)

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Which of the following is the inverse of y = 12 Superscript x? y = log Subscript one-twelfth Baseline x y = log Subscript 12 Bas
wariber [46]

Answer:

y = lnx/ln12

Step-by-step explanation:

Given the function y = 12^x, to find the inverse of the function, we news to write x as a function of y as shown:

Given y = 12^x

Taking ln of both sides

ln y = ln 12^x

ln y = xln12

Divide both sides by ln12

lny/ln12 = xln12/ln12

x = lny/ln12

x = ln(y-12)

Replacing y with x and x with y

The inverse of the function will be:

y = lnx/ln12

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1- Solution using graphs:
Take a look at the attached images.
The red graph represents the first given function while the blue graph represents the second given function.
We can note that the two graphs are the same line (they overlap).
This means that any chosen point on one of them will satisfy the other.
This means that there are infinite number of solutions to these two equations.

2- Solution using substitution:
The first given equation is:
y = -5x + 3 ...........> equation I
The second given equation is:
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Substitute with I in II and solve as follows:
2(-5x+3) + 10x = 6
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Hope this helps :)

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