Question

Find the inverse function in slope-intercept form (mx+b):
f(x)=5/3x+5

Answer 1

is this
\[f(x)=\frac{5}{3}x+5\]?

Answer 2

Yes, I need helpp.

Answer 3

ok we can do this
it is just like solving
\[\frac{5}{3}x+5=7\] more or less

Answer 4

but this is more general
start with
\[y=\frac{5}{3}x+7\] then switch \(x\) and \(y\) to write
\[x=\frac{5}{3}y+7\] and then solve for \(y\)
it will take two steps

Answer 5

How would i start solving it like that ?

Answer 6

\[x=\frac{5}{3}y+7\] subtract \(7\) from both sides to get
\[x-7=\frac{5}{3}y\] multiply by 3 and get
\[3x-21=5y\] divide by \(5\) to get
\[\frac{3x-21}{5}=y\]

Answer 7

and that is your inverse:
\[f^{-1}(x)=\frac{3x-21}{5}\]

Answer 8

oh if you want it in "slope intercept" form write it as
\[f^{-1}(x)=\frac{3}{5}x-\frac{21}{5}\]

Answer 9

The correct answer was 3/5x-3

Answer 10

did i make a mistake somewhere?

Answer 11

oh my fault there is no seven in the problem
it is
\[x=\frac{5}{3}y+5\]

Answer 12

ok same idea
\[x-5=\frac{5}{3}y\]
\[3x-15=5y\]
\[\frac{3x-15}{5}=y\] or
\[y=\frac{3}{5}x-3\]