Given f(x) = x^2 – 3 and g(x) = x+2/x . find (g ° f)(4).
a. 11/13
b. 6
c. 15/13
d. -6

C

Step-by-step explanation:

Given the two functions, we need to find

(g ° f)(4)

This means, we need to put the function f(x) INTO the function g(x) and then evaluate that new function at x = 4.

We put the whole expression of f(x) into "x" of g(x). Shown below:

Now we plug in 4 into x and evaluate:

Thus,

correct answer is C

(-1,-0.5)

step-by-step explanation:

(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