Answer:
Step-by-step explanation:
I'll use y instead of f(x):
The inverse of y [f(x)] = 3[tex]x^{2}[/tex] - 5 is
x = 3[tex]y^{2}[/tex] - 5
Rearrange to isolate y:
[tex]y^{2}[/tex] = (x+5)/3
For f(43) we get:
[tex]y^{2}[/tex] = (43+5)/3
[tex]y^{2}[/tex] = (48)/3
[tex]y^{2}[/tex] = 16
y = 4
==========
Since g(x) = x+1 and h(x)= x^2,
h(g(x)) = (x+1)^2
(x+1)^2
x^2 + 2x + 1
---------------
This is set equal to 3x^2 + x - 5 and we can then solve for x:
3x^2 + x - 5 = x^2 + 2x + 1
2x^2 -x -6 = 0
(x-2)(2x+3) = 0
The solutions are:
x = -3/2 and x = 2
