If f(x) = x2 + 2x - 1 and g(x) = 2x - 3, then find fog(x) and gof(x). | Basic Mathematics 2081.2

Basic Mathematics2081.210 marksNumerical: composite functions, maxima minimaLocal extrema and critical points

If $f(x) = x^2 + 2x - 1$ and $g(x) = 2x - 3$ , then find $fog(x)$ and $gof(x)$ . Find the local maxima and local minima of the function $f(x) = 3x^4 - 4x^3 - 12x^2 + 5$ . [5+5]

If $f(x) = x^2 + 2x - 1$ and $g(x) = 2x - 3$, then find $fog(x)$ and $gof(x)$. Find the local maxima and local minima of the function $f(x) = 3x^4 - 4x^3 - 12x^2 + 5$. [5+5]

$f(x) = x^2 + 2x - 1$ - $g(x) = 2x - 3$ - $f(x) = 3x^4 - 4x^3 - 12x^2 + 5$ (for Part 2) --- $fog(x) = f(g(x)) = f(2x-3)$ Substitute $(2x-3)$ into $f$ : $= (2x-3)^2 + 2(2x-3) - 1$ $= (4x^2 - 12x + 9) + (4x - 6) - 1$ $= 4x^2 - 8x + 2$ $gof(x) = g(f(x)) = g(x^2 + 2x - 1)$ Substitute

$f(x) = x^2 + 2x - 1$ - $g(x) = 2x - 3$ - $f(x) = 3x^4 - 4x^3 - 12x^2 + 5$ (for Part 2) --- $$fog(x) = f(g(x)) = f(2x-3)$$ Substitute $(2x-3)$ into $f$: $$= (2x-3)^2 + 2(2x-3) - 1$$ $$= (4x^2 - 12x + 9) + (4x - 6) - 1$$ $$= 4x^2 - 8x + 2$$ $$gof(x) = g(f(x)) = g(x^2 + 2x - 1)$$ Substitute

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If f(x) = x2 + 2x - 1 and g(x) = 2x - 3, then find fog(x) and gof(x). Find the local maxima and local minima of the function f(x) = 3x4 - 4x3 - 12x2 + 5. [5+5]