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]

mathstudent55 · Answer

$f(x) = x^2 − 4x + 7$

$f(x) = x^2 − 4x ~~~~~~~~~~~~~+ 7$

You need to put in the blank the term that completes the square of $x^2 - 4x$. Then you need to subtract from the 7 at the end of the line.

mathstudent55 · Answer

Do you know how to complete a square?

anonymous · Answer

Yeah. Actually it's part 3 I don't know how to do. Could u help with that bit please.?

mathstudent55 · Answer

f = hg
h = f/g
$h(x) = \dfrac{f(x)}{g(x)} $

anonymous · Answer

Thanks