Question

Find the inverse: h(x)=1/4(x-1)

Answer 1

\[ h(x) = \frac{1}{4(x-1)} \]

Whatever the form is, write y = h(x) and then solve for x, x = j(y). Then j will be the inverse of h.

Answer 2

Your choice of the function's name is different. Never seen someone named a function j.

Answer 3

Im still confused though.

Answer 4

http://www.wolframalpha.com/input/?i=inverse%28h%28x%29+%3D+1%2F%284%28x-1%29%29%29

Answer 5

JamesJ is telling you to solve for y\[x=\frac{1}{4(y-1)}.\]:)

Answer 6

It's the reflection of \(h(x) \) across the line y=x

Answer 7

Suppose f(x) = x - 1. What is the inverse that function?

Answer 8

i think it would be x+1

Answer 9

Yes. Now if we had written y = f(x) = x - 1, then this is the same as solving for x
If y = x-1, then x = y+1. Hence the inverse function is g(x) = x+1.

Answer 10

Try another. If f(x) = 2/x, what's the inverse. Write y = f(x) = 2/x. Now solve for x.

Answer 11

ok let me see

Answer 12

is it x=2*y or x=2/y ?

Answer 13

y = 2/x
xy = 2
x = 2/y.

Answer 14

So what is the inverse function of f(x) = 2/x ?

Answer 15

g(x)=2/y

Answer 16

g(x) = 2/x. Make sure the variables match.

Answer 17

Now let's verify this. If g is the inverse function, then f(g(x)) = x and g(f(x)) = x. Let's check.

f(g(x)) = f(2/x) = 2/(2/x) = 2x/2 = x. So that works.

Likewise
g(f(x)) = g(2/x) = 2/(2/x) = 2x/2 = x.

Answer 18

Now try this one. f(x) = 1/(x+1). What's the inverse of this function?

Answer 19

ok let me see

Answer 20

x=0

Answer 21

that can't possibly be right. Try again. Follow the method
Step 1: Write y = f(x)
Step 2: Solve this equation for x, i.e., find the function g so that x = g(y)
Step 3: The inverse function of f is now g(x)
Step 4: (optional) Verify the result by checking to make sure f(g(x)) = x and g(f(x)) = x.

Answer 22

x=1/(y-1) ?

Answer 23

Let's check. If g(x) = 1/(x-1) is the inverse of f(x) = 1/(x+1), then f(g(x)) = x.

Well
f(g(x)) = f(1/(x-1))
\[ = \frac{1}{1/(x-1) - 1} \]
\[ = \frac{x-1}{1 - (x-1)} \]
\[ = \frac{x-1}{-x} \]
well, that's not equal to x. So look like g(x) = 1/(x-1) isn't the inverse.

Answer 24

Let's try that again. y = f(x) = 1/(x+1)

Answer 25

my brain feels blocked

Answer 26

Solve for x.
y = 1/(x+1)
1/y = x + 1
x + 1 = 1/y
x = 1/y - 1

Answer 27

Hence the inverse function to f(x) = 1/(x+1) is g(x) = (1/x) - 1.

Answer 28

Following?

Answer 29

yes

Answer 30

Let's verify:
\[ f(g(x)) = f((1/x) - 1) = \frac{1}{(1/x - 1) + 1} = \frac{1}{1/x} = x \]
So it's looking good.

Answer 31

oh ! i see. you are switching the variables and sign, so its like the opposite

Answer 32

Ok. Now do your problem. h(x)=1/4(x-1). Follow the steps.

Answer 33

If y = h(x)
y = 1/4(x-1)

Now solve for x.

Answer 34

\[ y = \frac{1}{4(x-1)} \]

Answer 35

umm , x=1/4y+1

Answer 36

im never going to understand this.

Answer 37

Yes, x = (1/4y) + 1. Hence the inverse function g(x) = what?

Answer 38

Inverse function g(x) = (1/4x)+1

Answer 39

Correct. Now let's verify. h(x)=1/4(x-1)
h(g(x)) = h((1/4x) + 1)
\[ = \frac{1}{4((1/4x) + 1) - 4} = \frac{1}{1/x + 4 - 4} = \frac{1}{1/x} = x \]

Answer 40

So yes, h(g(x)) = x, the identity function. Therefore g is indeed the inverse of h.

Answer 41

ok great, i think i got it now

Answer 42

ok

Answer 43

thanks for your help