If f(x) = x2 - 1, g(x) = 2x + 1, find fog and gof and domain of fog. | Mathematics I 2077

Mathematics I20775 marksNumerical: Function compositionCombination of functions

If $f(x) = x^2 - 1$ , $g(x) = 2x + 1$ , find $fog$ and $gof$ and domain of $fog$ . [5]

If $f(x) = x^2 - 1$, $g(x) = 2x + 1$, find $fog$ and $gof$ and domain of $fog$. [5]

$f(x) = x^2 - 1$ $g(x) = 2x + 1$ Required: $fog$ , $gof$ , and domain of $fog$ . --- $fog(x) = f(g(x)) = f(2x+1)$ Replace $x$ in $f(x)=x^2-1$ with $(2x+1)$ : $fog(x) = (2x+1)^2 - 1$ $= 4x^2 + 4x + 1 - 1$ $\boxed{fog(x) = 4x^2 + 4x}$ --- $gof(x) = g(f(x)) = g(x^2 - 1)$ Replace $x$ in

$$f(x) = x^2 - 1$$ $$g(x) = 2x + 1$$ Required: $fog$, $gof$, and domain of $fog$. --- $$fog(x) = f(g(x)) = f(2x+1)$$ Replace $x$ in $f(x)=x^2-1$ with $(2x+1)$: $$fog(x) = (2x+1)^2 - 1$$ $$= 4x^2 + 4x + 1 - 1$$ $$\boxed{fog(x) = 4x^2 + 4x}$$ --- $$gof(x) = g(f(x)) = g(x^2 - 1)$$ Replace $x$ in

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