Inverse function

[albusd]

It asks me to find the expression for the inverse function of f(x)= Log1/2 (x+1) --- 1/2= Base, (x+1)= Argument

I thought it was f(x)= 1/2^(x+1) but it's not. It is f(x)=(1/2)^x + 1

Why? Sorry if this is the wrong place to post this.

 

[srmichael]

It asks me to find the expression for the inverse function of f(x)= Log1/2 (x+1) --- 1/2= Base, (x+1)= Argument

I thought it was f(x)= 1/2^(x+1) but it's not. It is f(x)=(1/2)^x + 1

Why? Sorry if this is the wrong place to post this.

It's not $\displaystyle f(x)=\dfrac{1}{2}^{x}+1$ either. Why do you think it is that? Is that what your teacher or book or friend said? In most cases, you can find the inverse of a function by either solving for x in the original equation or equivalently, as most people do, switch x and y in the original equation and then solve for y.

Do you know how to rewrite the following using exponents: $\displaystyle log_{b}(y)=x$

 

[albusd]

It's not $\displaystyle f(x)=\dfrac{1}{2}^{x}+1$ either. Why do you think it is that? Is that what your teacher or book or friend said? In most cases, you can find the inverse of a function by either solving for x in the original equation or equivalently, as most people do, switch x and y in the original equation and then solve for y.

It is what my book says.

Do you know how to rewrite the following using exponents: $\displaystyle log_{b}(y)=x$

b^x=Y

 

[albusd]

Correction

Sorry, I checked again and the book says f(x)= (1/2)^x - 1 . Not +.

Still, I don't get it.

 

[albusd]

Finally

I think I got it. Tell me if I'm wrong:

f(x)= Log1/2 (x+1)

y= Log1/2 (x+1) <=> 1/2^y = x+1

1/2^y = x+1
1/2^y - 1 = X

f^-1(x) = 1/2^x -1

 

[srmichael]

I think I got it. Tell me if I'm wrong:

f(x)= Log1/2 (x+1)

y= Log1/2 (x+1) <=> 1/2^y = x+1

1/2^y = x+1
1/2^y - 1 = X

f^-1(x) = 1/2^x -1

BINGO! You got it!

 

[HallsofIvy]

The function $\displaystyle f(x)= log_{1/2}(x+ 1)$ tells us to do two things: first add 1 to x, then take the logarithm, base 1/2. The inverse function must do the opposite things in the opposite order: first take 1/2 to the x power then subtract 1.