Question

Given the two functions f(x)=x2 - 4x +1 and g(t)=1- t

Find & Simplify f(g(t))

Answer 1

Explanation:

Given the two functions f(x)=x² - 4x +1 and g(t)=1-t

To simplify the composite function f(g(t)), we will replace x with (1-t) in f(x) as shown:

f(g(t)) = f(1-t)

f(1-t) = (1-t)²-4(1-t)+1

Expand the parenthesis

f(1-t) = 1-2t+t²-4+4t+1

f(1-t) = t²-2t+4t+1+1-4

f(1-t) = t²+2t-2

Hence the simplified form of f(g(t)) is t²+2t-2