poochybear
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Function Combinations and Compositions
- Thread starter poochybear
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Dr.Peterson
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If your textbook doesn't provide an explanation for these concepts (combinations of functions, composition of functions, and inverse functions), and helpful examples, you can find lessons online. We aren't really set up to give you complete lessons.
Here are some starting points:
Operations with Functions
www.mathsisfun.com
Composition of Functions
www.mathsisfun.com
Inverse Functions
www.mathsisfun.com
What are the 4 function operations? (w/ examples)
Operating on functions means doing arithmetic with the formula for two functions; that is, you add, subtract, multiply, or divide the two functions.
www.purplemath.com
Function Composition Using Only Sets of Points
Suppose f and g are sets of ordered pairs. To compose f with g, pick an x-value in g and find the corresponding y-value. Plug this, as x, into f.
www.purplemath.com
Inverse relations and how to find them
To invert a relation that is a list of points, just swap the x- and y-values of the points. To see if the inverse is a function, check the x-values.
www.purplemath.com
Once you have a clue, please show us your attempt, starting with just the first problem, and we can work with you.
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For reference, this is the exercise in the original post:
Q2. Solve the following problems:
(a) Define functions [imath]f(x) = \sqrt{x+1}[/imath], [imath]g(x) = x^2 - 2[/imath], and [imath]h(x) = \arcsin(x^3)[/imath]. Find (i) the expressions of [imath]f(x)g(x) + h(x)[/imath] and [imath]\frac{f(x)}{h(x)}[/imath]; (ii) the expression for composite function [imath](g\circ h)(x)[/imath]; and (iii) the largest possible domain of the function [imath]y = \frac{\sqrt{x^2-1}}{x^2-4}[/imath]. Please simplify your solutions.
(b) Let function [imath]f(x) = \sqrt[3]{2x^3+5}[/imath] and [imath]Dom(f) = (0,\infty)[/imath]. Given that [imath]f(x)[/imath] is strictly increasing, find a formula for the inverse function [imath]f^{-1}[/imath].
Q2. Solve the following problems:
(a) Define functions [imath]f(x) = \sqrt{x+1}[/imath], [imath]g(x) = x^2 - 2[/imath], and [imath]h(x) = \arcsin(x^3)[/imath]. Find (i) the expressions of [imath]f(x)g(x) + h(x)[/imath] and [imath]\frac{f(x)}{h(x)}[/imath]; (ii) the expression for composite function [imath](g\circ h)(x)[/imath]; and (iii) the largest possible domain of the function [imath]y = \frac{\sqrt{x^2-1}}{x^2-4}[/imath]. Please simplify your solutions.
(b) Let function [imath]f(x) = \sqrt[3]{2x^3+5}[/imath] and [imath]Dom(f) = (0,\infty)[/imath]. Given that [imath]f(x)[/imath] is strictly increasing, find a formula for the inverse function [imath]f^{-1}[/imath].