Question

The function is defined by f(x) = ax + b for x ER, where a and b are constants. It is given that f(2)= 1 and f(5) = 7. ii) Solve them and find the values of a and b. 1) Solve the equation f(f(x)) = 0. 1) Set up a pair of simultaneous equations using the information given.

Answer 1

ii)

$$1=a(2)+b$$

$$7=a(5)+b$$

$$a=slope=\dfrac{7-1}{5-2}=2$$

$$b=1-2(2)=-3$$

$$a=2, b=-3, y=2x-3$$

1)

$$f(f(x))=0$$

$$a(ax+b)+b=0$$

$$a^2x+ab+b=0$$

$$x=-\dfrac{ab+b}{a^2}$$

$$x=-\dfrac{2(-3)-3}{(2)^2}$$

$$x=\dfrac{9}{4}$$