Answer the following questions related to inverse functions.

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Answer the following questions related to inverse functions. (i) Define an inverse function. State the necessary and sufficient condition for a real-valued function to possess an inverse. (ii) Give reasons to show that the function

g(x)=x^{3}+7

is invertible on

\mathbb{R}

whereas the function

h(x)=x^{2}

is not invertible on

\mathbb{R}

. (iii) Describe the Horizontal Line Test. By referring to the graphs of

y=x^{3}

and

y=x^{2}

, explain how this test helps to decide whether the corresponding functions are invertible.

Related theory

Functions
Functions and invertibility
Relations and Functions
Algebra
Invertible functions and inverse of a function
Exponential and Logarithmic Functions

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