Question

f(x)=(ax+b)/(cx+d), abcd are constants. If ad=bc, show that f is a constant function.

Answer 1

oh here

Answer 2

we can do this quickly if we get to use calculus

Answer 3

yes we can

Answer 4

ok then take the derivative, say "oh look it is zero" and therefore your function must be a constant. would you like me to write it out?

Answer 5

if you have time thx

Answer 6

\[f'(x)=\frac{(cx+d)a-(ax+b)c}{(cx+c)^2}\]
\[=\frac{acx+ad-acx-bc}{(cx+d)^2}=\frac{ad-bc}{(cx+d)^2}\] and since
\[ad-bc=0\] you get
\[f'(x)=0\] for all x making f a constant

Answer 7

k thx dude