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If g(3x-2) = 7x-15 , find the value of g–¹og(2)​

User Kam Sen
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To find the value of g^(-1) o g(2), we need to determine the input value that would produce an output of 2 when fed into the function g(x).

Let's begin by finding the inverse function of g(x). We can start by replacing g(x) with y in the equation and then solving for x.

Given:

g(3x - 2) = 7x - 15

Replacing g(x) with y:

y = 7x - 15

Now, let's solve for x in terms of y:

y = 7x - 15

y + 15 = 7x

x = (y + 15) / 7

Therefore, the inverse function g^(-1)(x) is:

g^(-1)(x) = (x + 15) / 7

Now we can find g^(-1) o g(2) by plugging g(2) into g^(-1)(x):

g^(-1) o g(2) = g^(-1)(g(2))

= g^(-1)(7(2) - 15)

= g^(-1)(14 - 15)

= g^(-1)(-1)

Plugging -1 into g^(-1)(x):

g^(-1)(-1) = (-1 + 15) / 7

= 14 / 7

= 2

Therefore, the value of g^(-1) o g(2) is indeed 2.


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User Bruna
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