Inverse Functions Practice Questions

Last Updated : 08 Aug, 2024

Inverse functions are those functions which reverse the actions of another function and reversing its operation. It swaps input and output values, allowing for the retrieval of the original input from a given output.

This article consist of a series of Inverse Functions Practice Questions focused at strengthening your understanding and proficiency in this fundamental concept of Inverse functions.

Table of Content

What are Inverse functions
Inverse function of Some Common Functions
Inverse Functions Practice Questions - Solved
Inverse Functions Practice Questions - Unsolved
Inverse Functions Practice Questions - FAQs

What are Inverse functions

The inverse function is inverse of a function.

let f be a function then f⁻¹ represents the inverse of function (f), such that:

f{f⁻¹ (y)} = y for all y ∈ Range (f)

and

f⁻¹{f(x)} = x for all x ∈ Domain(f)

Graph of an inverse function is a reflection of the original function across the line y = x.

If f(x) = log x then its inverse is, f^-1(x) = e^x and the graph for the same is added below:

logarithm-and-exponential-graph — Inverse Functions

To graph the inverse function, interchange the roles of x and y. If the original graph passes through (a, b), the inverse graph will pass through (b, a).

Inverse function of Some Common Functions

Inverse function of some common functions are added in the table below:

Function	Inverse Function	Domain of Function	Range of Inverse Function
f(x) = x+a	f⁻¹(x) = x−a	All real numbers	All real numbers
f(x) = x-a	f⁻¹(x) = x+a	All real numbers	All real numbers
f(x) = ax (a≠0)	f⁻¹(x) = x/a	All real numbers	All real numbers
f(x) = x/a (a≠0)	f⁻¹(x) = ax	All real numbers	All real numbers
f(x) = x²	f⁻¹(x) = √x	x ≥ 0	x ≥ 0
f(x) = √x	f⁻¹(x) = x²	x ≥ 0	x ≥ 0
f(x) = x³	f⁻¹(x) = ∛x	All real numbers	All real numbers
f(x) = ∛x	f⁻¹(x) = x³	All real numbers	All real numbers
f(x) = ln(x)	f⁻¹(x) = e^x	x > 0	All real numbers
f(x) = e^x	f⁻¹(x) = ln(x)	All real numbers	x > 0
f(x) = sin(x)	f⁻¹(x) = arcsin(x)	−π/2 ≤ x ≤ π/2	−1 ≤ x ≤ 1
f(x) = cos(x)	f⁻¹(x) = arccos(x)	0 ≤ x ≤ π	−1≤ x ≤ 1
f(x) = tan(x)	f⁻¹(x) = arctan(x)	−π/2 < x < π/2	All real numbers