Question

The function is defined by ( ) for , where and are constants. It 

is given that ( ) and ( ) 

i) Set up a pair of simultaneous equations using the information given.

ii) Solve them and find the values of and .

iii) Solve the equation ( ( )) .

Answer 1

The function f is defined by f(x) = ax + b for x € R, where a and b are constants. It

is given that f(2) = 1 and f(5) = 7.

i) Set up a pair of simultaneous equations using the information given.

ii) Solve them and find the values of a and b.

iii) Solve the equation f(f(x)) = 0.

Solution.

i)

$2a+b=1$

$5a+b=7$

ii)

$3a=6$

$a=2,b=1-2a=1-4=-3$

$f(x)=2x-3$

iii)

$f(f(x)) =2(2x-3)-3$

$2(2x-3)-3=4x-9=0$

$x=9/4=2.25$