Question

Se f(x)= 2x-3/2 e gof(x)= 4x2-3, determine g(x)

Answer 1

$2f(x) = 2x - 3 \\ x = \frac{2f(x) + 3}{2}$

$f(x) = \frac{2x - 3}{2} \\ g(f(x)) = 4 {x}^{2} - 3$

$g(f(x)) = 4. {( \frac{2f(x) + 3}{2}) }^{2} - 3 \\ g(f(x)) \\ = 4. \frac{4 {f(x)}^{2} + 12f(x) + 9}{4} - 3$

$4 {f(x)}^{2} + 12f(x) + 9 - 3 \\ = 4 {f(x)}^{2} + 12f(x) + 6$

$g(f(x)) = 4 {f(x)}^{2} + 12f(x) + 6$

$g(x) = 4 {x}^{2} + 12x + 6$