Question

Find the inverse function of f(x)=1/x+5
f-1(x)=__________________? help

Answer 1

f^-1(x) = (1/x) - 5

Answer 2

@royrdz look at other answer it was wrong

Answer 3

be careful here ok?

Answer 4

it is not
\[\frac{1}{x}-5\] it is
\[\frac{1}{x-5}\]

Answer 5

First of all you must know that not all functions have inverses. Therefore to verify you must us the following statement: if
f(a)=f(b)
then
a=b
Now just plug in the statement and you have that
\[1/a +5 = 1/b +5\]
which by simple arithmetic you have that
a=b
which states that the function has an inverse. Now to find the inverse you just substitute
x
by
f−1(x)
and
f(x)
by
x
which in this case is the following:
\[x = 1/f^{-1}(x) + 5\]
and clear for the inverse function:
\[x - 5 = 1/f ^{-1}(x)\]
;
\[1/(x-5) = f ^{-1}(x)\]
which is the result you needed. Hope it helps form the beautiful island of Puerto Rico. Peace, Love and Happiness

Answer 6

\[y=\frac{1}{x}+5\] switch x and y get
\[x=\frac{1}{y}-5\] solve for y get
\[x+5=\frac{1}{y}\]
\[y=\frac{1}{x+5}\] so
\[f^{-1}=\frac{1}{x-5}\]

Answer 7

what jobh said

Answer 8

\[f-1 ( x ) = (1\div x) -5\]

Answer 9

\[f ^{-1}(y)=(1-5y)/y, i.e. f ^{-1}(y)=(1/y)-5\]