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IrinaK [193]
3 years ago
13

I'm so lost. I have no clue.

Mathematics
2 answers:
tiny-mole [99]3 years ago
7 0
I supppose the answer is F(X)=X²+4, you can use the vertex to confirm.
ziro4ka [17]3 years ago
6 0

Answer: F(x) = x2 + 3 ;)

Step-by-step explanation:

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[Will mark as brainliest]
Aleks04 [339]

The answer is: f^{-1} = 4x^2-3,\quad\text{for  } x \leq 0

The inverse of a function f(x) is another function, f^{-1}(x), with the following property:

f(f^{-1}(x)) = f^{-1}(f(x)) = x

In other words, the inverse of a function does exactly "the opposite" of what the original function does, and so if you compute them both in sequence you return to the starting point.

Think for example to a function that doubles the input, f(x)=2x, and one that halves it: f(x)= \frac{x}{2}. Their composition is clearly the identity function f(x)=x, since you consider "twice the half of something", or "half the double of something".

In general, to invert a function y=f(x), you have to solve the expression for x, writing an expression like x = g(y). If you manage to do so, then g is the inverse of f.

In your case, you have

f(x) = y = -\frac{1}{2}\sqrt{x+3}

Multiply both sides by -2 to get

-2y = \sqrt{x+3}

Square both sides to get

4y^2 = x+3

Finally, subtract 3 from both sides to get

x = 4y^2 - 3

Since the name of the variables doesn't really have a meaning, you can say that the inverse function is

f^{-1}(x) = 4x^2 - 3

As for the domain of the inverse function, remember what we said ad the beginning: if the original function goes from set A (domain) to set B (codomain), then the inverse function goes from set B (domain) to set A (codomain). This means that the inverse function is defined on an element in B if and only if that element belongs to the range of the original function, i.e. the set of the elements of the codomain b \in B such that there exists a \in A : f(a)=b. So, we need the range of f(x).

We know that the range of g(x)=\sqrt{x} is [0,\infty). When you transform it to g(x)=\sqrt{x+3} you simply translate the graph horizontally, so the range doesn't change. But when you multiply the function times -\frac{1}{2} you affect both extrema of the range, turning it into (-\infty,0], which you can simply write as x \leq 0

4 0
3 years ago
I need a bit help im new to this math stuff
kompoz [17]

Answer:

I think it is the 3rd one

3 0
3 years ago
110 decreased by 70%
Bess [88]
110x0.7= 77
110-77= 33
so 33 is your answer
7 0
2 years ago
What is the leading coefficient? - 3x3 + 8x2 + 9x - 4
postnew [5]

Answer:

c

Step-by-step explanation:

the highest exponent is 3 so the leading coefficient is -3

6 0
3 years ago
Read 2 more answers
Pls help me in this question it is really needed
DaniilM [7]

Answer:

6 1/8 ×10 2/7= 60

60÷2 1/3= 30

The answer:

30

8 0
3 years ago
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