Solving for x and Inverse Functions in Terms of y

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In summary, the conversation discusses the function f defined by y=f(x) = 3ln4x with a domain of 0.01<=x<=1. The conversation then asks to solve for x in terms of y to find the inverse function f^-1(x), write down the domain of f^-1, plot f from x=0.01 to x=1 and plot f^-1 on the same axes, and describe the geometric relationship between f and f^-1. The person asking for assistance is confused with functions and needs help understanding the basic rules and definitions, including the inverse function of ln(x).
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fazal
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Homework Statement




The function f is defined by y=f(x) = 3ln4x 0.01<=x<=1

a)Solve for x in terms of y and hence find the formula for the inverse function f^-1(x)

b)Write down the domain of f^-1

c)Plot f from x =0.01 to x=1 and than plot f^-1 on the same axes but only for domain values of x given by the range of f

d)Describe the geometric relationship that you can see between f and f^-1

plse assist as iam very confused with functions...!

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Then start by reviewing the definitions and basic rules. What is the inverse function to ln(x)?
 

FAQ: Solving for x and Inverse Functions in Terms of y

How do you solve for x in terms of y?

To solve for x in terms of y, you need to isolate the variable x on one side of the equation. This can be done by using algebraic operations such as addition, subtraction, multiplication, and division. Once x is isolated, the equation will be in the form x = y + (numbers and/or other variables).

What does it mean to solve for x in terms of y?

Solving for x in terms of y means finding the value of x that makes the equation true when substituted into the equation. This means that the value of x is dependent on the value of y, and the equation is written in terms of y.

Can you give an example of solving for x in terms of y?

Yes, for example, if the equation is x + y = 10, then to solve for x in terms of y, you would subtract y from both sides of the equation to get x = 10 - y. This means that the value of x is equal to 10 minus the value of y.

Why is it important to solve for x in terms of y?

Solving for x in terms of y is important because it allows us to find the relationship between x and y in an equation. This can be useful in various scientific fields such as physics, chemistry, and engineering, where equations often involve multiple variables.

Are there any tips for solving x in terms of y?

Yes, a helpful tip is to always start by isolating the variable x on one side of the equation. This can be done by using inverse operations (e.g. adding the opposite of a number, multiplying by the reciprocal). Additionally, it is important to pay attention to the order of operations and to simplify the equation as much as possible before substituting values for y.

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