Question

función inversa de h(x)=1/x+4

Answer 1

Función inversa:

Procedimiento:

$h(x) = \frac{1}{x} + 4 \\ \\ y = \frac{1}{x} + 4 \\ \\ x = \frac{1}{y} + 4 \\ \\ \frac{1}{y} + 4 = x \\ \\ \frac{1}{y} = x - 4 \\ \\ 1 = (x - 4)y \\ \\ 1 = xy - 4y \\ \\ xy - 4y = 1 \\ \\ (x - 4)y = 1 \\ \\ y = \frac{1}{x - 4} \\ \\ h ^{ - 1} (x) = \frac{1}{x - 4}$

Resultado:

$h ^{ - 1} (x) = \frac{1}{x - 4}$