Question

let f(x)=(x+4)/(x+10) f^-1=(-9)

Answer 1

Answer:  -9.4

Step-by-step explanation:

$f(x)=\dfrac{x+4}{x+10}\\\\\\\text{To find the inverse, swap the x's and y's, then solve for y}\\\\\\x=\dfrac{y+4}{y+10}\\\\\\x(y+10)=y+4\\\\xy+10x=y+4\\\\xy-y=4-10x\\\\y(x-1)=4-10x\\\\\\y=\dfrac{4-10x}{x-1}$

$f^{-1}(-9)=\dfrac{4-10(-9)}{-9-1}\\\\\\.\qquad \qquad =\dfrac{4+90}{-10}\\\\\\.\qquad \qquad =\dfrac{94}{-10}\\\\\\.\qquad \qquad =\large\boxed{-9.4}$