Question

QF Q6.) Find the function for b.

Answer 1

(g₀f)(x)=g(f(x))
=g(2x-4)
=4(2x-4)^2-3
=4(4x^2-16x+16)-3
=16x^2-64x+61

Answer 2

The function notation f(x)=2x-4 means replace the x on the right-hand side with the value in parentheses on the left.
For example, f(y)=2y-4; f(4)=2(4)-4=4; f(1)=2(1)-4=-2 and so on.
The same principle applies to g(x), for example
g(2)=4(2^2)-3=13,
g(x+1)=4(x+1)^2-3=4(x^2+2x+1)-3=4x^2+8x+4-3=4x^2+8x+1
and so on.

(g of f)(x) is another way to write g(f(x)), therefore
g(f(x))
=g(2x-4)   [because f(x)=2x-4
=4(2x-4)^2-3
=4(4x^2-16x+16)-3
=16x^2-64x+64-3
=16x^2-64x+61