Inverse Functions
Math ⇒ Functions
Inverse Functions starts at 11 and continues till grade 12.
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See sample questions for grade 11
Find the inverse of f(x) = (x - 4)/5.
Given f(x) = 4x - 7, find f⁻¹(x).
If f(x) = √(x - 1), what is the domain of f⁻¹(x)?
If f(x) = 1/(x - 2), what is f⁻¹(x)?
If f(x) = 1/(x + 2), what is the domain of f⁻¹(x)?
If f(x) = 1/x, what is f⁻¹(x)?
If f(x) = 2x - 3, and g(x) = (x + 3)/2, what is g(f(4))?
If f(x) = 2x + 1, and f⁻¹(x) = (x - 1)/2, what is f⁻¹(f(7))?
Which of the following functions has an inverse that is also a function?
(1) f(x) = x²
(2) f(x) = x³
(3) f(x) = |x|
(4) f(x) = sin(x)
Which of the following functions is its own inverse?
(1) f(x) = x
(2) f(x) = 1/x
(3) f(x) = -x
(4) All of the above
Which of the following is NOT a necessary condition for a function to have an inverse?
(1) The function must be one-to-one.
(2) The function must be onto.
(3) The function must be defined for all real numbers.
(4) The function must be continuous.
Which of the following is the correct process to find the inverse of a function?
(1) Replace x with y, solve for y, then swap x and y.
(2) Replace y with x, solve for x, then swap x and y.
(3) Replace x with y, solve for x, then swap x and y.
(4) Replace y with x, solve for y, then swap x and y.
A function f(x) is invertible if and only if it is ________.
A function must be ________ to have an inverse that is also a function.
The domain of the inverse function f⁻¹(x) is the ________ of the original function f(x).
The range of the inverse function f⁻¹(x) is the ________ of the original function f(x).
Given f(x) = 2x + 1, and g(x) = (x - 1)/2, are f and g inverses of each other?
If f(x) = 2x + 3, and h(x) = 2x - 3, are f and h inverses of each other?
If f(x) = x + 2, and g(x) = x - 2, are f and g inverses of each other?
True or False: The function f(x) = x² is invertible for all real numbers.
