f(x) = { x + 5}/ { x + 10 }
f^{-1}( -3 ) =?
brief steps would be wonderful!

Question

f(x) = { x + 5}/ { x + 10 }
f^{-1}( -3 ) =?
brief steps would be wonderful!

anonymous · Answer

$$x=\frac{y+5}{y+10}$$ sovle for y

anonymous · Answer

$$x(y+10)=y+5$$
$$xy+10x=y+5$$
$$xy-y=5-10x$$
$$y(x-1)=5-10x$$
$$y=\frac{5-10x}{x-1}$$

anonymous · Answer

They really need another way to write inverse function than f(x)^-1. I get the two confused all the time. >.>

You know, like there's arcsin for sin(x)^-1

anonymous · Answer

oh you want 
$$f^{-1}(-3)$$ so now you have a choice. replace x by -3 in the above solution, or start with 
$$\frac{x+5}{x+10}=-3$$ and solve for x. 
steps will be the same, except you will get a number rather than an expresson in y

anonymous · Answer

$$x+5=-3(x+10)$$
$$x+5=-3x-30$$
$$4x=-35$$
$$x=-\frac{35}{4}$$ which is just what you would get writing 
$$f^{-1}(-3)=\frac{5-10(-3)}{-3-1}$$

anonymous · Answer

thank u  really helped simplify it so i could understand it