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Please explain your answer as well. THX!!

Please explain your answer as well. THX!!-example-1
Please explain your answer as well. THX!!-example-1
Please explain your answer as well. THX!!-example-2
User Gianfranco
by
8.3k points

1 Answer

4 votes

Answer:

The correct option is the fourth one.

Explanation:

FIRST QUESTION:

To solve this problems we need to know the following things:

1. Given f(x) = k*g(x). We know that the graph of f(x) will be identical to the graph of g(x) but enlarged or compressed depending on the value of k.

2. Given f(x) = g(x) + k. We know that the graph of f(x) will be identical to the graph of g(x) but shift downwards if k<0 or shift upwards if k>0.

Having said this, we have that:

f(x) = 1/2 * log_2 (x) - 8

In this case, there are two transformations: The function is supressed by 1/2 and also shifted downwards by 8 units.

SECOND QUESTION

We need to find the portion of domain where f(x) = x^2 + a is one-to-one.

A function f is one-to-one if each x in the domain has exactly one image in the range. And, no y in the range is the image of more than one x in the domain.

So if we want a one-to-one function we need to restrict the domain starting from x=0. So it would be: [0, inf)

Now to find the inverse function, we need to solve the equation for "x"

y = x^2 + a

y - a = x^2

x = sqrt(y-a)

Then, the inverse function would be:

y = sqrt(x-a)

The correct option is the fourth one.

User Rharper
by
7.9k points

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