# Function notations/inverse functions.

• Nov 29th 2008, 09:31 AM
Function notations/inverse functions.
Hello,
I can't solve this maths question and I would really appreciate your help.
My problem is:

Let f(x) =
__ (this means "square root of x" - I didn't know how to type it!)
V x

and g(x) = 2^x. Solve the equation

(f^-1 o g)(x) = 0.25.

Thanks.
• Nov 29th 2008, 09:56 AM
masters
Quote:

Hello,
I can't solve this maths question and I would really appreciate your help.
My problem is:

Let f(x) =
__ (this means "square root of x" - I didn't know how to type it!)
V x

and g(x) = 2^x. Solve the equation

(f^-1 o g)(x) = 0.25.

Thanks.

$f(x)=\sqrt{x}$

$g(x)=2^x$

$f^{-1}(x)\rightarrow x=\sqrt{y} \rightarrow y=x^2$

$\left[f^{-1} \circ g\right](x)=(2^x)^2=2^{2x}$

$2^{2x}=.25$

$2^{2x}=\frac{1}{4}$

$2^{2x}=\frac{1}{2^2}$

$2^{2x}=2^{-2}$

$2x=-2$

$x=-1$
• Nov 29th 2008, 10:35 AM
Shyam
Quote:

Hello,
I can't solve this maths question and I would really appreciate your help.
My problem is:

Let f(x) =
__ (this means "square root of x" - I didn't know how to type it!)
V x

and g(x) = 2^x. Solve the equation

(f^-1 o g)(x) = 0.25.

Thanks.

$f(x) = \sqrt{x}$

$y = \sqrt{x}$

For $f^{-1}(x)$, interchange, x and y and solve for y

$x = \sqrt{y}$

$x^2=y$

$y= x^2$

$f^{-1}(x)=x^2\;\;\;\;and\;\;\;\;g(x)=2^x$

Now,

$(f^{-1}\;\;o\;\;g)(x)=(2^x)^2$

$(2^x)^2=0.25$

$2^{2x}=2^{-2}$

$(because,\;\; 0.25=\frac{1}{4}=\frac{1}{2^2}=2^{-2})$

$2x=-2$

$x=-1$

did you get it now???
• Nov 29th 2008, 10:37 AM