f(x)=1-3^x
the graph of f is reflected over the line y=x. what is the name of function of the new graph?

Question

saifoo.khan · Answer

i think that will be a straight line through which this will be reflected.

anonymous · Answer

the inverse 0.o

anonymous · Answer

f¯¹(x)

saifoo.khan · Answer

i have no idea.

anonymous · Answer

y = 1-3^x
x = 1-3^y 
then solve for y.. I.. don't know how to do that for this problem...

anonymous · Answer

you are going to have to use logarithms

anonymous · Answer

$$ \log_{3}\left| -x+3 \right| =\log_{3}3^y$$$$y=\log_{3}\left| -x+3 \right|$$ I think I could be very very wrong lol

anonymous · Answer

saifoo its add maths funtion

dumbcow · Answer

$$y = 1 - 3^{x}$$
switch variables
$$x = 1-3^{y}$$
solve for y
$$3^{y} +x = 1$$
$$3^{y} = 1-x$$
$$\log 3^{y} = \log (1-x)$$
$$y*\log 3 = \log(1-x)$$
$$y = \frac{\log (1-x)}{\log 3}$$

anonymous · Answer

what is the name of function of the new graph?
no name

dumbcow · Answer

$$f^{-1}(x)$$

anonymous · Answer

f(x)$$=1-3^x$$
f(x)=y
$$f(y)^{-1}=x$$
y=1-3^x
1-y=3^x
$$\log_{3}(1-y)=x $$

$$f(y)^{-1}=x$$
$$f(y)^{-1}$$=$$\log_{3}(1-y)$$
if u insert x instead of y
$$f(x)^{-1}$$=$$\log_{3}(1-x)$$