Suppose that the function g and its derivative with respect to...

Question

Suppose that the function g and its derivative with respect to x have the following values at x=0, 1, 2, 3, and 4.

Assuming the inverse function g^(-1) is differentiable, find the slope of g^(-1)(x) at

a. x=1

Table showing values of a function g and its derivative g' at x = 0 to 4 for finding the inverse function's slope at x=1.

Accepted Answer

Welcome back, everyone. Evaluate the slope of F inverts of X at X equals 2/3 using the table given below. A 3 halves, B 97, C 14th, and D 79s. For this problem, if we want to evaluate the slope of the inverse function, let's remember the formula. Specifically, that formula will represent derivatives which are Representative of slopes. So the inverse. Of F of X. Derivative is equal to 1 divided by the derivative of the original function at a point, which is F inverse of X. This is the formula that we want to use. And we know that X is equal to 2/3, so we can rewrite this formula. As F inverse derivative at x equals 2/3 is equal to 1 divided by the derivative of F at F inverse of 2/3. So now, let's focus on the right-hand side of the equation and specifically we can begin by finding F inverse of 2/3. Let's suppose that it is some value A. If we take F of both sides, we can show that 2/3 is equal to F of A. Because F of F inverts returns us the actual value 2/3 on the left hand side. On the right hand side, we just get F of A. So what does this equation mean? Well, it basically tells us that the value of the function is 2/3 at some X coordinate A. So we are going to use the second row of the table where it says F of X, those are the values of the function. And we want to locate 23s. So we have 2/3. And we Can use this table to identify the X coordinate F at 4 is equal to 2/3, right? Based on the table, we can show that F of 4 is equal to 2/3, and therefore, A is equal to 4. And now we can simplify our expression, right, we get 1 divided by the derivative of F at. Or, because F inverse at 2/3 is equal to A, which is 4. So now the final value that we want to find is the derivative of F at X equals 4. Using the table, we identify X equals 4 and we go down until we reach the third row where it says F of X. So F at 4 is equal to 7 lines, meaning we take 1 and divide by 7 lines. The reciprocal of 7 9s is 97. So the answer to this problem corresponds to the answer choice B. Thank you for watching.

Suppose that the function g and its derivative with respect to x have the following values at x=0, 1, 2, 3, and 4.Assuming the inverse function g^(-1) is differentiable, find the slope of g^(-1)(x) ata. x=1

Watch next

Suppose that the function g and its derivative with respect to x have the following values at x=0, 1, 2, 3, and 4.
Assuming the inverse function g^(-1) is differentiable, find the slope of g^(-1)(x) at
a. x=1