Fill in the table: f(x) = sin(x) f(x) = cos(x) f(x) =tan(x) Domain Restriction of Domain of Range of f (x) to make inverse Inverse f-¹ (z) Inverse f-¹ (z) I 1 I

Q: The tan (x) function can be differentiated using the product rule. true or false

A: The tan (x) function can be differentiated using the product rule.

Q: Differentiate. f(x) = x cos(x) sin(x) (please write it out on paper)

A:

Q: Verify using Composition of functions that f(x)= 2x+5 and g(x)= (1/2)x - (5/2) are inverse functions…

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Q: 2. Graph of y = f(x): 3 -2 -1- y=f(x) 1 2 3 6 7 -2 -3 4,

A: Consider the given graph: a) Since, the graph is not smooth and there are corners at x = 1, 4.…

Q: Use algebra to find the inverse of the function f(x) = x + 1. The inverse function is f'(x) = - 1

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Q: Determine whether f and g are inverse functions by evaluating (f o g)(x) and (g o f)(x). f(x) =…

A: The function f and g are f(x) = x6+7x g(x) = 6x1-7x we have to determine whether each pair  of…

Q: Find a suitable substitution for evaluating ∫tan x sec2 x dx andexplain your choice.

A: we have to integrate the following integral using a suitable substitution. ∫tanx.sec2xdx

Q: dx as a function of x if dt Find dt2 x sin x. dt?

A: We will solve the following

Q: list the three transformations being applied to f(x)= 4 sin(4(x-5))+5 parent function: f(x)=sinx

A: To find- List the three transformations being applied to fx = 4sin4x - 5 + 5.  Parent function: fx =…

Q: 3. Find the inverse function f-¹(x) of f(x)=3 sin 2x

A: The given function is: fx=3sin2x   To calculate the inverse function of the given function…