Transformation of Graphs
The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.
Exponential Functions
The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.
(3) For the functions f(x) = 3x − 4 and g(x) = x + 2, find the following and determine the domain in each case: (a) g((f)) (b) fg (c) f/g
(4) For the functions f(x) = √x − 3 and g(x) = √x + 2, find and determine the domain in each case: (a) gf (b) f + g
(5) For the functions f(x) =3/x − 4 and g(x) =3/x+ 4, find f(g(x)) and g(f(x)), hence or otherwise determine whether g(x) is the inverse of f(x).
(6)
(a) Using the remainder theorem, determine whether (x − 4) and (x − 1) are factors of the expression x3 + 3 x2 − 22 x − 24 .
(b) Hence, by use of long division, find all remaining factors of the expression.
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