If f(x) = 3x + 10 and g(x) = x^2 - 1,then (fo | vedclass

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(A) Given $f(x) = 3x + 10$ and $g(x) = x^2 - 1$. First,find the composite function $(fog)(x) = f(g(x))$. $(fog)(x) = f(x^2 - 1) = 3(x^2 - 1) + 10$. $(

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$\left(\frac{x-7}{3}\right)^{\frac{1}{2}}$

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(A) Given $f(x) = 3x + 10$ and $g(x) = x^2 - 1$. First,find the composite function $(fog)(x) = f(g(x))$. $(fog)(x) = f(x^2 - 1) = 3(x^2 - 1) + 10$. $(fog)(x) = 3x^2 - 3 + 10 = 3x^2 + 7$. Let $y = (fog)(x) = 3x^2 + 7$. To find the inverse,solve for $x$ in terms of $y$: $y - 7 = 3x^2$. $x^2 = \frac{y - 7}{3}$. $x = \pm \sqrt{\frac{y - 7}{3}}$. Replacing $y$ with $x$,we get $(fog)^{-1}(x) = \sqrt{\frac{x - 7}{3}} = \left(\frac{x - 7}{3}\right)^{\frac{1}{2}}$.

If $f(x) = 3x + 10$ and $g(x) = x^2 - 1$,then $(fog)^{-1}(x) = $

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