Use a right triangle to write the following expression in algebraic expression. assume that x is positive and in the domain of the given inverse trigonometric function. tan(cos−1(9x))=

The algebraic expression for

Step-by-step explanation:

Let θ = use the properties of inverse trigonometric functions

In a right angled triangle, the cosine of an angle is

Use this expression  to find what are the sides of the right triangle.

Next find what is the expression for the opposite side, for this use the Pythagorean theorem and the values above

We said that , so now we can use the definition of tangent and the right triangle that we defined to find the algebraic expression for

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1