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Composite Functions Calculator

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Example
Created on 2024-06-20Asked by Theodore Sanchez (Solvelet student)
Find (fg)(x) (f \circ g)(x) where f(x)=x2+1 f(x) = x^2 + 1 and g(x)=3x+2 g(x) = 3x + 2 .

Solution

Step 1: Identify the functions f(x)=x2+1 f(x) = x^2 + 1 and g(x)=3x+2 g(x) = 3x + 2 . Step 2: Find (fg)(x) (f \circ g)(x) : (fg)(x)=f(g(x))=f(3x+2). (f \circ g)(x) = f(g(x)) = f(3x + 2). Step 3: Substitute g(x) g(x) into f(x) f(x) : f(3x+2)=(3x+2)2+1. f(3x + 2) = (3x + 2)^2 + 1. Step 4: Simplify the expression: (3x+2)2+1=9x2+12x+4+1=9x2+12x+5. (3x + 2)^2 + 1 = 9x^2 + 12x + 4 + 1 = 9x^2 + 12x + 5. Step 5: Conclusion. The composite function (fg)(x)=9x2+12x+5 (f \circ g)(x) = 9x^2 + 12x + 5 . Solved on Solvelet with Basic AI Model
Some of the related questions asked by Daniel Lee on Solvelet
1. Find the derivative of the composite function h(x)=(sin(x))2 h(x) = (\sin(x))^2 2. Evaluate the composite function g(f(x)) g(f(x)) for f(x)=3x22x f(x) = 3x^2 - 2x and g(x)=ex g(x) = e^x .,
DefinitionComposition or composite function is a function that results from applying one function to the output of another. The idea of a composition of two functions f of g is a form of combination of two functions such that one function takes an input and output is supplied to other function mean f(g(x)) where we are giving output of g as an input to f. so is known as composite function (as one are composed on other ) are utilized widely in areas like calculus, algebra and functional analysis as imperative part to represent sequential processes & transformations. They are used to describe intricate correlations of variable and to scrutinize array of system behavior. In other words, if f(x)=x2 and g(x)=sin(x) then let us consider the function h(x)=f(g(x)). The composite function f◦g is f(g(x))=(sin(x))2, which is the square of the sine function.
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