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Anvisha [2.4K]
4 years ago
11

Consider the tables that represent ordered pairs corresponding to a function and its inverse. When comparing the functions using

the values in the table, which conclusion can be made? According to the tables, f(x) does not have a y-intercept. According to the tables, f–1(x) does not have an x-intercept. The domain of f(x) is restricted such that x ≥ 0, so the domain of f–1(x) is restricted such that y ≥ 0. The range of f(x) includes values such that y ≥ 1, so the domain of f–1(x) includes values such that x ≥ 1.

Mathematics
2 answers:
lara31 [8.8K]4 years ago
5 0

Answer:

D)The range of f(x) includes values such that y ≥ 1, so the domain of f–1(x) includes values such that x ≥ 1.

Step-by-step explanation:

The missing tables are:

First table  

x:    0  1    2

f(x): 1   10  100

Second table

x:         1000   100   10

f^-1(x):  3          2       1  

Option A is not correct because f(x) has a y-intercept at (0, 1)

If f(x) has a y-intercept, then f^-1(x) has a x-intercept, which is located at (1, 0). Then option B is not correct

Option C is not correct because the domain of f^-1(x) is associated with x values.

Option D is correct because the domain of f(x) is the range of f^-1(x) and vice versa

Tasya [4]4 years ago
3 0

Answer: D

The range of f(x) includes values such that y ≥ 1, so the domain of f–1(x) includes values such that x ≥ 1.

Step-by-step explanation:

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If the function f (x) has a domain of (a,b] and a range of [c,d), then what is the domain and range of g (x) = m × f (x) + n?
xz_007 [3.2K]
<h3>Answer: Choice A</h3>

Domain = (a,b]

Range = [mc + n,md + n)

==============================================

Explanation:

The domain stays the same because we still have to go through f(x) as our first hurdle in order to get g(x).

Think of it like having 2 doors. The first door is f(x) and the second is g(x). The fact g(x) is dependent on f(x) means that whatever input restrictions are on f, also apply on g as well. So going back to the "2 doors" example, we could have a problem like trying to move a piece of furniture through them and we'd have to be concerned about the f(x) door.

-------------------

The range will be different however. The smallest value in the range of f(x) is y = c as it is the left endpoint. So the smallest f(x) can be is c. This means the smallest g(x) can be is...

g(x) = m*f(x) + n

g(x) = m*c + n

All we're doing is replacing f with c.

So that means mc+n is the starting point of the range for g(x).

The ending point of the range is md+n for similar reasons. Instead of 'c', we're dealing with 'd' this time. The curved parenthesis says we don't actually include this value in the range. A square bracket means include that value.

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