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kodGreya [7K]
3 years ago
5

Can some0ne help me?

Mathematics
2 answers:
xxMikexx [17]3 years ago
6 0

g(x) = 3x + 2

y = 3x + 2

x = 3y + 2

3y = x - 2

y = x/3 - 2/3

inverse g(x) = (x - 2) / 3

g(x) = 4 - 5x

y = 4 - 5x

x = 4 - 5y

5y = 4 - x

y = 4/5 - x/5

inverse g(x) = (4 - x) / 5

PtichkaEL [24]3 years ago
4 0

Answer:

(x - 2)/3

(x - 4)/-5 or (-x + 4)/5

Step-by-step explanation:

this is an inverse function, and to solve an inverse function you would :

swap x and g(x) without bringing the x coefficient with it, just simply swap the variables. Then, solve for g(x), and that's it

the first question's answer is :

g(x) = 3x + 2

x = 3(g(x)) + 2

x - 2 = 3(g(x))

(x - 2)/3 = g(x)

the second one is:

g(x) = 4 - 5x

x = 4 - 5(g(x))

x - 4 = -5(g(x))

(x-4)/-5 = g(x)

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Step-by-step explanation:

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What is the effect on the graph of the function f(x) = x^2 when f(x) is changed to f(x − 6)
olya-2409 [2.1K]

Answer:

The comparison graph is also attached in 3rd figure. In the 3rd figure, the graph with vertex (0, 0) is representing f(x) = x^2 and \:f\left(x\right)=\left(x-6\right)^2 is represented as being shifted 6 units to the right as compare to the function f(x) = x^2.

Step-by-step explanation:

When we Add or subtract a positive constant, let say c, to input x, it would be a horizontal shift.  

For example:

Type of change               Effect on y = f(x)

y = f(x - c)                      horizontal shift: c units to right

So

Considering the function

f(x) = x^2

The graph is shown below. The first figure is representing f(x) = x^2.

Now, considering the function

\:f\left(x\right)=\left(x-6\right)^2

According to the rule, as we have discussed above, as a positive constant 6 is added to the input, so there is a horizontal shift, 6 units to the right.

The graph of \:f\left(x-6\right)=\left(x-6\right)^2 is shown below in second figure. It is clear that the graph of  \:f\left(x-6\right)=\left(x-6\right)^2  is shifted 6 units to the right as compare to the function f(x) = x^2.

The comparison graph is also attached in 3rd figure. In the 3rd figure, the graph with vertex (0, 0) is representing f(x) = x^2 and \:f\left(x\right)=\left(x-6\right)^2 is represented as being shifted 6 units to the right as compare to the function f(x) = x^2.

5 0
3 years ago
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