What is the inverse of f(x)=(x+6)2 for x≥–6 where function g is the inverse of function f?

Sorry my mistake, it is actually worded as "f(x) =(x+6)^2"

Explanation:

y

=

(

x

+

6

)

2

with  

x

≥

−

6

, then

x

+

6

is positive, so

√

y

=

x

+

6

And  

x

=

√

y

−

6

for  

y

≥

0

So the inverse of  

f

is

g

(

x

)

=

√

x

−

6

for  

x

≥

0

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240