Calc BC Problem. No random answers plz

Part A)

Part B)

Step-by-step explanation:

Please refer to the table of values.

Part A)

A. 1)

We want to find f(1).

According to the table, when x=1, f(x)=2.

Hence, f(1)=2.

A. 2)

We want to find f⁻¹(1).

Notice that when x=0, f(x)=1.

So, f(0)=1.

Then by definition of inverses, f⁻¹(1)=0.

A. 3)

We want to find f’(1).

According to the table, when x=1, f’(x)=1.4.

Hence, f’(1)=1.4.

A. 4)

We will need to do some calculus.

Let g(x) equal to f⁻¹(x). Then by the definition of inverses:

Take the derivative of both sides with respect to x. On the left, this will require the chain rule. Therefore:

Solve for g’(x):

Substituting back f⁻¹(x) for g(x) yields:

Therefore:

We already determined previously that f⁻¹(1) is 0. Therefore:

According to the table, f’(0) is 0.7. So:

Hence, (f⁻¹)’(1)=10/7.

Part B)

We want to find the equation of the tangent line of y=f⁻¹(x) at x=4.

First, let’s determine the points. Since f(2)=4, this means that f⁻¹(4)=2.

Hence, our point is (4, 2).

We will now need to find our slope. This will be the derivative at x=4. Therefore:

We know that f⁻¹(4)=2. So:

Evaluate:

Now, we can use the point slope form. Our point is (4, 2) and our slope at that point is 5/14.

So:

Solve for y:

Adding 2 to both sides yields:

Hence, our equation is:

answer is more than one

step-by-step explanation:

(0,,,0)

step-by-step explanation:

the table of x and y values is shown in the attached pic(part of question)

we have to decide according that graph

given points are (0, 0) (–1, 0), (2, 0)

when we graph these points on graph they show an increasing line as shown in the attached pic