Answer:
f(x).f(x) [tex]=\frac{25}{36} x^2 +\frac{25}{9}x+\frac{25}{9}[/tex]
Step-by-step explanation:
Given f(x) is a linear function.
Let f(x)= ax+c
given,f(-2)=0
∴a(-2)+c=0
⇔-2a +c=0
⇔c=2a ..........(1)
Again f(4) = -5
∴a.4+c=-5
⇔4a+c=5
⇔4a +2a=5 [∵ c= 2a]
⇔6a=5
⇔[tex]a=\frac{5}{6}[/tex]
Putting the value of a in equation (1)
[tex]c=2 \times \frac{5}{6}[/tex]
[tex]\Leftrightarrow c= \frac{5}{3}[/tex]
Therefore f(x) [tex]=\frac{5}{6} x+\frac{5}{3}[/tex]
f(x).f(x)
[tex]=(\frac{5}{6} x+\frac{5}{3})(\frac{5}{6} x+\frac{5}{3})[/tex]
[tex]=(\frac{5}{6} x+\frac{5}{3})^2[/tex]
[tex]=\frac{25}{36} x^2 +\frac{25}{9}x+\frac{25}{9}[/tex]
