L5-6 Inverse Relations and Functions

Identify the inverse function of f(x) = 2x + 3.

• f^-1(x) = 3 - 2x

• f^-1(x) = (x - 3) / 2

• f^-1(x) = (x + 3) / 2

• f^-1(x) = 2x - 3

Answer explanation

Identify the inverse function by switching x and y, then solving for y. The correct choice is f^-1(x) = (x - 3) / 2.

Find the inverse of g(x) = 4x - 5.

• y = (x - 5) / 4

• y = 4 / (x - 5)

• y = (x + 5) / 4

• y = 5 - 4x

Answer explanation

The inverse of g(x) is found by switching x and y, then solving for y. So, y = (x + 5) / 4 is the correct choice.

Verify if h(x) = 3x - 2 and its inverse are indeed inverses algebraically.

• Yes

• Maybe

• Sometimes

• No

Answer explanation

The functions h(x) = 3x - 2 and its inverse are indeed inverses algebraically because they undo each other's operations, confirming the correct answer choice 'Yes'.

Graph the inverse function of y = 2x + 1.

• y = (x + 1) / 2

• y = (x - 1) / 2

• y = x / 2 + 1

• y = 2x - 1

Answer explanation

The correct inverse function of y = 2x + 1 is y = (x - 1) / 2. To find the inverse, switch x and y, then solve for y.

Explain the domain and range restrictions for the inverse of a function.

• The domain of the inverse function is the range of the inverse function.

• The range of the inverse function is the range of the original function.

• The domain of the inverse function is the domain of the original function.

• The domain of the inverse function is the range of the original function, and the range of the inverse function is the domain of the original function.

Answer explanation

The domain of the inverse function is the range of the original function, and the range of the inverse function is the domain of the original function.

Solve the equation f(f(x)) = x for the function f(x) = 5x - 4.

• x = 5

• x = 8

• x = 6

• x = 3

Answer explanation

The function f(x) = 5x - 4 is its own inverse, so f(f(x)) = x. Therefore, x = 6 is the correct answer.

Identify the inverse function of y = 3/x.

• y = -3/x

• y = 3/x

• y = x/3

• y = 1/3x

Answer explanation

The inverse function of y = 3/x is y = 3/x itself. Inverse function swaps x and y, but in this case, the function remains the same.

Calculate the inverse of the function k(x) = x^2 + 1.

• k^(-1)(x) = ±√(x^2 - 1)

• k^(-1)(x) = ±√(x + 1)

• k^(-1)(x) = ±√(x - 1)

• k^(-1)(x) = ±(x - 1)

Answer explanation

The correct inverse function of k(x) = x^2 + 1 is k^(-1)(x) = ±√(x - 1) because to find the inverse, switch x and y then solve for y.

Show algebraically that the function p(x) = x^3 - 2x and its inverse are inverses.

• The function p(x) = x^3 - 2x and its inverse are inverses.

• The inverse of p(x) is p^(-1)(x) = x^3 + 2x.

• p(x) = x^3 - 2x is not a function.

• The function p(x) = x^3 - 2x and its inverse are not inverses.

Answer explanation

The function p(x) = x^3 - 2x and its inverse are inverses because they undo each other's operations, confirming the correct answer choice.

Graph the inverse function of y = 1/(x - 2).

• y = 1/(x - 1)

• y = 1/(x + 2)

• y = 1/x + 2

• y = 1/x - 2