How Do You Solve Composite Inverse Functions?

[kings13]

Homework Statement

Use the functions below to find the indicated value.

Homework Equations

f(x)=1/5x - 3

http://www.webassign.net/cgi-bin/symimage.cgi?expr=f(x) = 1/5 x - 3

g(x)=x^2http://www.webassign.net/cgi-bin/symimage.cgi?expr=g(x) = x^2

(g^-1 o f^-1)(-3)=

i presume the o means multiply (wrong)

The Attempt at a Solution

y=5(x+3)

y=root(x)

15xroot(x)+45root(x)

completely wrong.

 

[jgens]

The hollow circle denots the composition of functions, not the product. Second, you should be more precise with your notation. For example, I'm unsure whether f(x) = x/5 - 3 or f(x) = (5x)^-1 - 3.

 

[kings13]

I linked to the exact picture of the problems. anyone who can solve this is greatly appreciated

 

[jgens]

Okay, so f(x) = x/5 -3. Now, do you know how to find the composition of two functions? For example, if I told you to find f(g(x)), could you do it?

 

[kings13]

yea it would be 1/5(x^2) - 3. right? What next??

 

[jgens]

Okay, so you just need to find g^-1(f^-1(-3)). Pretty simply.

 

[kings13]

so i got 5 (-3+3) aka 5(0)=0

so inverse g (0)=root 0??

is that my answer?

 

[kings13]

yep! the program took the answer correctly! thanks so much