Question

given f(x) = 1-2x, and g(x) = x^2+1, find:

a) g(-2) ---- i get 5 ?

b) f(x+1)

c) g`f(x) --- there is like a degree symbol circle between g and f..

d) f^-1(x)

Answer 1

a) correct

b) put (x+1) instead of x in f(x),
f(x+1)=1-2(x+1)=1-2x-2=-2-2x

c) g o f(x) (reads g of f(x))
means
g(f(x))
=g(1-2x)
=(1-2x)²+1
=1-4x+4x²+1
=2-4x+4x²
=2(1-2x+2x²)

d) f^-1(x)
the inverse of f(x).
follow the following steps to find the inverse.
1. write f(x)=1-2x as
y=1-2x
2. switch the symbols x and y
x=1-2y
3. solve for y in terms of x to get the inverse.