Answer:
15. h⁻¹ (x) = 5x-6/2
16. (g.f)x = 4x^2 -2x -1
Explanation:
15. Find Inverse of h(x) = 2x+6 /5
Let y = 2x+6/5 we need to find value of x
Multiplying both sides with 5
5y = 2x+6
Adding -6 on both sides
5y -6 = 2x
Dividing both sides by 2
5y-6/2 = x
Now replace y with x our answer will be:
h⁻¹ (x) = 5x-6/2
16. f(x) =2x-1 and g(x) = x^2 -2 find (g.f)x
(g.f)x can be written as: g(f(x))
We know f(x) = 2x-1 so, put value of f(x) into x of g(x).
Putting values we get:
(g.f)x = g(f(x))= (2x-1)^2 -2
= 4x^2 -2x +1 -2
= 4x^2 -2x -1
so, (g.f)x = 4x^2 -2x -1