Solved: Given that f(x)=2x+3 and g(x)=x^2-2 find the composite function f(g(x)). Enter your answe [Math]
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Given that f(x)=2x+3 and g(x)=x^2-2 find the composite function f(g(x)). Enter your answer as a function of x:|x □ Your answer is currently: x

Given that f(x)=2x+3 and g(x)=x^2-2 find the composite function f(g(x)). Enter your answer as a function of x:|x □ Your answer is currently: x

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2x2−12x^{2}-1
1 Identify the given functions: f(x)=2x+3 and g(x)=x2−2g(x)=x^{2}-2
2 To find f(g(x)) , substitute g(x) into f(x) . So, f(g(x))=f(x2−2)f(g(x)) = f(x^{2}-2)
3 Replace x in f(x) with x2−2x^{2}-2 to get f(g(x))=2(x2−2)+3f(g(x)) = 2(x^{2}-2) + 3
4 Distribute the 2 into the parentheses: 2(x2−2)=2x2−42(x^{2}-2) = 2x^{2} - 4
5 Add 3 to the result from
6 2x2−4+3=2x2−12x^{2} - 4 + 3 = 2x^{2} - 1 .
So, the composite function f(g(x)) is 2x2−12x^{2}-1 .
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