Question

dadas las funciones f(x)= 2x/3 - 1 y g(x)= 2x-6 determina:

3[2g(4)-5f(3)] : 5f(2) - 3/4
​

Answer 1

Respuesta:

Explicación paso a paso:

Hallamos f(3):

$f(x)= \frac{2x}{3} - 1\\\\f(3)= \frac{2(3)}{3} - 1\\\\f(3)= \frac{6}{3} - 1\\\\f(3)= 2 - 1\\\\f(3)=1$

Hallamos f(2):

$f(x)= \frac{2x}{3} - 1\\\\f(2)= \frac{2(2)}{3} - 1\\\\f(2)= \frac{4}{3} - 1\\\\f(2)= \frac{4-3}{3} \\\\f(2)=\frac{1}{3}$

Hallamos g(4):

$g(x)= 2x-6\\\\g(4)=2(4)-6\\\\g(4)=8-6\\\\g(4)=2$

Hallamos lo que nos piden:

$\frac{3\left[ 2g(4)-5f(3)\right]}{5f(2)} -\frac{3}{4} \\\\\frac{3\left[ 2(2)-5(1)\right]}{5(\frac{1}{3} )} -\frac{3}{4} \\\\\frac{3[4-5]}{\frac{5}{3} } -\frac{3}{4} \\\\\frac{-3}{\frac{5}{3} } -\frac{3}{4} \\\\\frac{-9}{5} -\frac{3}{4} \\\\\frac{-9\times 4-5\times 3}{20} \\\\\frac{-36-15}{20} \\\\-\frac{51}{20}$