f(x)=(2x-3)
(gof)(x)=4x2-16x+18
g(x)...?
Try g(x)=x^2-2x+3
aw thank you so much.
so, how do to write with step?
(gof)(x)=4x2-16x+8
(g(f(x))=4x2-16x+8
and then?
To find the function g(x), we can substitute the function f(x) into the function (gof)(x).
Given that (gof)(x) = 4x^2 - 16x + 18, and f(x) = 2x - 3, we substitute f(x) into (gof)(x):
(gof)(x) = 4(f(x))^2 - 16(f(x)) + 18
Substitute f(x) = 2x - 3 into the above equation:
(gof)(x) = 4(2x - 3)^2 - 16(2x - 3) + 18
Now, expand and simplify this expression to find g(x).
Step 1: Expand (2x - 3)^2
(gof)(x) = 4(4x^2 - 12x + 9) - 16(2x - 3) + 18
Step 2: Simplify the expression
(gof)(x) = 16x^2 - 48x + 36 - 32x + 48 + 18
Step 3: Combine like terms
(gof)(x) = 16x^2 - 80x + 102
Therefore, g(x) = 16x^2 - 80x + 102.