The function f is defined by
f(x) = x2 − 4x + 7 for x 2.
(i) Express f(x) in the form (x − a)2 + b and hence state the range of f. [3]
(ii) Obtain an expression for f−1(x) and state the domain of f−1. [3]
The function g is defined by
g(x) = x − 2 for x 2.
The function h is such that f = hg and the domain of h is x 0.
(iii) Obtain an expression for h(x). [1]

Question

The function f is defined by
f(x) = x2 − 4x + 7 for x > 2.
(i) Express f(x) in the form (x − a)2 + b and hence state the range of f. [3]
(ii) Obtain an expression for f−1(x) and state the domain of f−1. [3]
The function g is defined by
g(x) = x − 2 for x > 2.
The function h is such that f = hg and the domain of h is x > 0.
(iii) Obtain an expression for h(x). [1]

anonymous · Answer

what is f?

anonymous · Answer

(i) (x-2)2+3

anonymous · Answer

Yes

anonymous · Answer

the range would be (3,infinity)

anonymous · Answer

(ii) f(x) = x2 − 4x + 6   domain all R

anonymous · Answer

(ii)$$f ^{-1}(x)=2+\sqrt{x-3}$$ the domain $$[3,\infty]$$