Question

Find formulas for the following inverse functions.
a. Let f(x) = 8 -2x Find f^-1(y)
b. g(t) = sqrt(2-t) Find g^-1(s)
c. f(t) = 1000e^0.2t Find f^-1(p)

Answer 1

I had similar problems on my exam and have no clue how to solve.

Answer 2

how would you solve
\[8-2x=7\]?

Answer 3

I remember that inverse is the opposite of y so I guess you are looking for x

Answer 4

I would subtract 8 from both sides and get -2x = -1 and then divide by -2

Answer 5

The word inverse is what I don't understand

Answer 6

right
a) subtract \(8\)
b) divide by \(-2\)

Answer 7

your inverse is therefore
\[f^{-1}(y)=\frac{y-8}{-2}\]

Answer 8

or if you prefer
\[f^{-1}(y)=\frac{8-y}{2}\] same thing

Answer 9

so is the problem just asking me to solve like I normally would do?

Answer 10

you can find it in your head, or you can also write
\[8-2x=y\] and solve for \(x\) via
\[8-2x=y\\
y-8=-2x\\
x=\frac{y-8}{-2}\\
f^{-1}(y)=\frac{y-8}{-2}\]

Answer 11

For b, I would have sqrt(2) = y + t

Answer 12

@satellite73

Answer 13

\[ g(t) = \sqrt{2-t} \]

Answer 14

how would you solve
\[\sqrt{2-t}=5\]?

Answer 15

you would square both sides

Answer 16

yes
giving \(2-t=5^2\) then what?

Answer 17

@satellite73 , is that right?

Answer 18

f^-1(y) = (2-t)^2

Answer 19

@sourwing

Answer 20

your answer above to the question is wrong
you are not done solving for \(t\) yet in \(\sqrt{2-t}=5\)
first step was right, square both sides to get
\[2-t=5^2\]

Answer 21

then subtract \(2\) and get
\[-t=5^2-2\] then change the sign and get
\[t=2-5^2\]

Answer 22

now we can solve
\[s=\sqrt{2-t}\]for \(t\)
square both sides
\[s^2=2-t\] subtract \(2\)
\[s^2-2=-t\] change the sign
\[2-s^2=t\] and your inverse is
\[g^{-1}(s)=2-s^2\]

Answer 23

(x)^2 = (sqrt(2-y))^2
x^2 = 2 - y
x^2 - 2 = -y

Answer 24

@satellite73