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Gr12 Mathematics: Ch 2.3 Linear Functions

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Gr12 Mathematics: Ch 2.3 Linear Functions

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Questions and Answers

What is the primary purpose of finding the inverse of a linear function?

To simplify the function

To find the domain and range of the function

To graph the function

To interchange the roles of the dependent and independent variables (correct)

What is the first step in finding the inverse of a linear function?

Express in function notation

Solve for y

Interchange x and y

Start with the function (correct)

What is the resulting form of the inverse of a linear function?

Exponential function

Quadratic function

Rational function

Linear function (correct)

What is the domain and range of the inverse function, assuming a ≠ 0?

Domain: ℝ, Range: ℝ (A) Signup and view all the answers

What is the formula for the inverse of a linear function, given y = ax + q?

y = 1/a x - q/a (C) Signup and view all the answers

What is the effect of interchanging the roles of the dependent and independent variables when finding the inverse of a linear function?

It swaps the domain and range of the function. (A) Signup and view all the answers

What is the result of solving for y in the equation x = ay + q?

y = (1/a)x - (q/a) (D) Signup and view all the answers

Why is the inverse of a linear function also a linear function?

Because the steps to find the inverse do not change the linearity of the function. (B) Signup and view all the answers

What is the purpose of expressing the inverse function in function notation?

To clearly distinguish it from the original function. (D) Signup and view all the answers

What can be said about the graph of the inverse of a linear function?

It is a line. (B) Signup and view all the answers

If f(x) = 2x + 3, what is the value of f^{-1}(5)?

4 (C) Signup and view all the answers

Given a linear function f(x) = ax + q, which of the following statements is TRUE about the graph of its inverse function?

It is a reflection of the original function across the line y = x. (A) Signup and view all the answers

What is the y-intercept of the inverse function of f(x) = 3x - 2?

-2/3 (A) Signup and view all the answers

If f(x) = -x + 1, what is the value of f^{-1}(-2)?

-3 (B) Signup and view all the answers

Given a linear function f(x) = ax + q, what can be said about the relationship between the slopes of f(x) and its inverse function?

They are multiplicative inverses. (B) Signup and view all the answers