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Consider the function 2. 1 3 x f (x) 5.1 Write down the equations of the asymptotes of f. (2) 5.2 Calculate the intercepts of the graph of f with the axes. (3) 5.3 Sketch the graph of f on DIAGRAM SHEET 1. (3) 5.4 Write down the range of y = f(x). (1) 5.5 Describe, in words, the transformation of f to g if 2. 1 3 x g(x) (2) [11]

Not all inverses of functions are also functions. Some inverses of functions are relations. If an inverse is not a function, then we can restrict the domain of the function in order for the inverse to be a function. To make the inverse a function, we need to choose a set of x-values in the function and work only with those.

A function must be a one-to-one relation if its inverse is to be a function. If a function \(f\) has an inverse function \(f^{-1}\), then \(f\) is said to be invertible. Given the function \(f(x)\), we determine the inverse \(f^{-1}(x)\) by: interchanging \(x\) and \(y\) in the equation; making \(y\) the subject of the equation;

GRADE 12 MATHEMATICS MASTER TUTORIAL 3 . FUNCTIONS and INVERSES. HANDED OUT: 1 MARCH 2024 DUE: 12 MARCH 2024 . NAME TEACHER ... FUNCTIONS INVERSES Linear, Quadratic, Exponential , Log and Hyperbola functions Transformations (reflections, translations, stretches)

Grd 12 Investigation 2025 - Free download as PDF File (.pdf), Text File (.txt) or read online for free. The document is an investigation for Grade 12 Mathematics focusing on functions and their inverses, with a submission deadline of February 16, 2024. It consists of three parts, covering types of relations, the inverse of exponential functions, and the conditions under which the inverse of a ...

This document provides instructions for a grade 12 mathematics investigation on functions and inverses. The investigation consists of five activities over nine pages. It aims to investigate the relationship between functions and their inverses. The first activity recaps the definitions of functions and conditions that determine whether a relation is a function. It includes examples of one-to ...

Inverses . Given the invertible function f(x), we determine the inverse f −1(x) by: – replacing every x with y and y with x; – making y the subject of the equation; – expressing the new equation in function notation. If we represent the function f and the inverse function f −1 graphically, the two graphs are reflected about the line y = x

Grade 12 Chapter 3 – Functions and Inverses. Posted on July 27, 2012 March 16, 2018 by Maths @ SHARP. Revise the straight line, hyperbola and parabola functions and then practice determining whether a given graph is a function and use this in the application of log graphs and exponential graphs.

Grade 12 Mathematics self-study guide covering Functions and Finance. Includes key concepts, formulas, and practice exercises for independent learning. ... (Subtract1from the p-value and add 3 to the q-value) y=2 x +1 (3) +2 45 Inverse function Learners must be able to determine, and sketches graph of inverse defined by: • y = ax + q • y ...

This document is for learners to investigate function and inverses at grade 12 level. This document, can be used as a different way to engage learners in learning a concept. This document will help teachers to lessen the burden of setting the formal task for investigation. This document is for learners to investigate function and inverses at ...

Mathematics video lessons, worksheets and learner manuals for Grade 12 Functions and Graphs. Functions. ... Functions Part 1(Inverse) Revise Nov 2023 Paper: Functions Part 2 (Quadratic and Hyperbola) Hyperbolic functions.

Interchange x and y and write the equation of inverse function f-1: . We now verify that the points (1 , 1) , (-1 , 0) and (-3 , -1) used above to sketch the graph of the inverse function are on the graph of f-1. . Question Let f(x) = x 2 - 4 x + 5, x ≤ 2. 1) Find the inverse function of f. 2) Find the domain and the range of f-1. Solution

We can say that the inverse function f –1 (x) = ½x – 3; Every point on the function has the same coordinates as the corresponding point on the inverse function, except that they are swapped around. Example: (–3; 0) on the function is reflected to become (0; –3) on the inverse function.

Grade 12 Mathematics Inverse Functions Solutions - Free download as PDF File (.pdf), Text File (.txt) or read online for free. This document provides exercises and solutions related to functions and inverse functions. It includes questions about determining if relations are functions, evaluating functions, finding domains and ranges, sketching graphs of functions and their inverses, and ...

Grade 12 Mathematics Investigation 2023 Page 4 of 9. 2 - INVESTIGATING FUNCTIONS AND THEIR INVERSES. If a function is called f ( )x then its inverse (only if it’s also a function, i. if it passes the vertical line test) is. denoted as f 1 x . The rule (equation) of the inverse of a function is obtained by interchanging/swopping x

Grade 12 – Functions. Aims and outcomes of tutorial: Improve marks and help you achieve 70% or more! ... Inverse Functions – video. 4 Inverse Functions – pdf. 5 Log and Exponential Functions – video. 6 Log and Exponential Functions – pdf. 7 Solving Cubic Expressions – video. 8 ...

Chapter 2: Functions. Learners must be encouraged to check whether or not the inverse is a function. It is very important that learners understand that \(f^{-1}(x)\) notation can only be used if the inverse is a function. Learners must not confuse the inverse function \(f^{-1}\) and the reciprocal \(\frac{1}{f(x)}\).

Siyavula's open Mathematics Grade 12 textbook, chapter 2 on Functions covering 2.7 Summary . Home Practice. For learners and parents For teachers and schools. Past papers Textbooks. ... and the inverse function \({f}^{-1}\) graphically, the two graphs are reflected about the line \(y=x\). The domain of the function is equal to the range of the ...

Grade 12 Investigation 2023 Inverse Functions - Free download as PDF File (.pdf), Text File (.txt) or read online for free. This document provides instructions for a Grade 12 mathematics investigation on functions and inverses. The investigation consists of 5 activities over 9 pages and takes 2 hours to complete. It is an individual task with no group work allowed.