Mathematics - Functions Question with Solution | TestHub

Given $2f\left(a\right)+3 f\left(c\right)=f\left(b\right)-f\left(d\right)$

Using fundamental principle of counting,

when $f\left(c\right)=0, f\left(a\right)=1 \text{then} f\left(b\right)-f\left(d\right)=2$ has $7$ choices,

Similarly when $f\left(c\right)=0, f\left(a\right)=2 \text{then} f\left(b\right)-f\left(d\right)$ has $5$ choices.

Counting like this we get the total number of one-one function as $31$