I Please need to this questions

Question

1.   If f(x) = 2x + 1 and g(x) = x², what is f ○ g? What is g ○ f?

2.   Consider f(x) = 2x + 3. Find the inverse of this function. Verbally, compare what f does to x (“multiply by 2, then add 3”) to what f^-1 does to x.

3.   Consider f(x) = x² + 3, x < 0. What is the inverse of this function?

Answer 1

For f(o)g this is equivalent to saying what is the value of the function f(x) when the input is g(x) which is x^2 so this is 2x^2 +1

Then g(o)f is the value of the function g(x) when the input is f(x) which is 2x+1 so this is

(2x+1)^2= 4x^2 +4x +1

To find the inverse of a function just swap x and y and resolve for y

To get The inverse of f(x) = 2x +3 swapping x and y gives us x=2y+3

2y = x-3

y = (x-3)/2

To get the inverse of f(x) = x^2 +3 we start with x =y^2 +3

x-3 = y^2

y=sq root of ( x-3) This functioned is only defined when x>or=3. if x< 3 you would have the square root of a negative number