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The inverse of a function (G(x)) can be found by switching the roles of (x) and (y) and solving for (y).
Given the function (G(x) = -\frac{4}{3}x + 2), let's find its inverse:
Step 1: Replace (G(x)) with (y):
[y = -\frac{4}{3}x + 2]
Step 2: Swap (x) and (y):
[x = -\frac{4}{3}y + 2]
Step 3: Solve for (y):
[x - 2 = -\frac{4}{3}y]
[-\frac{3}{4}(x - 2) = y]
So, the inverse function (G^{-1}(x)) is:
[G^{-1}(x) = -\frac{3}{4}(x - 2)]
What else can I help you with?
What is the relationships between inverse functions?
The inverse of the inverse is the original function, so that the product of the two functions is equivalent to the identity function on the appropriate domain. The domain of a function is the range of the inverse function. The range of a function is the domain of the inverse function.
Is the inverse of an exponential function the quadratic function?
No. The inverse of an exponential function is a logarithmic function.
If an inverse function undoes the work of the original function the original function's becomes the inverse function's domain?
The original function's RANGE becomes the inverse function's domain.
What is the inverse of a cubic function?
The inverse of the cubic function is the cube root function.
What is the inverse function of -6?
-6 is a number, not a function and so there is not an inverse function.
Why is x squared a inverse function?
X squared is not an inverse function; it is a quadratic function.
What is the inverse function of add 6?
The inverse function means the opposite calculation. The inverse function of "add 6" would be "subtract 6".
If an inverse function undoes the work of the original function what does the original function's becomes the inverse function's domain?
Range
Does every function have an inverse that is a function?
No. A simple example of this is y = x2; the inverse is x = y2, which is not a function.
If an inverse function undoes the work of the original function the original function's range becomes the inverse function's?
range TPate
Is an exponential function is the inverse of a logarithmic function?
No, an function only contains a certain amount of vertices; leaving a logarithmic function to NOT be the inverse of an exponential function.
What is an inverse of a function?
The opposite of another function - if you apply a function and then its inverse, you should get the original number back. For example, the inverse of squaring a positive number is taking the square root.
